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Journal articles on the topic 'Complete tripartite graphs'

Author: Grafiati

Published: 3 June 2025

Last updated: 22 June 2025

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1

Seoud, M. A., and M. Z. Youssef. "On labelling complete tripartite graphs." International Journal of Mathematical Education in Science and Technology 28, no. 3 (1997): 367–71. http://dx.doi.org/10.1080/0020739970280306.

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2

Revathi, R., D. Angel, and R. Mary Jeya Jothi. "MMD labeling of complete tripartite graphs." Journal of Physics: Conference Series 1770, no. 1 (2021): 012083. http://dx.doi.org/10.1088/1742-6596/1770/1/012083.

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3

Edwards, Keith. "Edge decomposition of complete tripartite graphs." Discrete Mathematics 272, no. 2-3 (2003): 269–75. http://dx.doi.org/10.1016/s0012-365x(03)00195-x.

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4

Haviland, Julie, and Andrew Thomason. "Rotation numbers for complete tripartite graphs." Graphs and Combinatorics 7, no. 2 (1991): 153–63. http://dx.doi.org/10.1007/bf01788140.

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5

Bunge, Ryan C. "On 1-rotational decompositions of complete graphs into tripartite graphs." Opuscula Mathematica 39, no. 5 (2019): 623–43. http://dx.doi.org/10.7494/opmath.2019.39.5.623.

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Consider a tripartite graph to be any simple graph that admits a proper vertex coloring in at most 3 colors. Let \(G\) be a tripartite graph with \(n\) edges, one of which is a pendent edge. This paper introduces a labeling on such a graph \(G\) used to achieve 1-rotational \(G\)-decompositions of \(K_{2nt}\) for any positive integer \(t\). It is also shown that if \(G\) with a pendent edge is the result of adding an edge to a path on \(n\) vertices, then \(G\) admits such a labeling.

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6

Camacho, Charles, Silvia Fernández‐Merchant, Marija Jelić Milutinović, et al. "Bounding the tripartite‐circle crossing number of complete tripartite graphs." Journal of Graph Theory 100, no. 1 (2021): 5–27. http://dx.doi.org/10.1002/jgt.22763.

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7

Chiang, N. P. "Chaotic Numbers of Complete Bipartite Graphs and Tripartite Graphs." Journal of Optimization Theory and Applications 131, no. 3 (2006): 485–91. http://dx.doi.org/10.1007/s10957-006-9152-2.

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8

Bunge, Ryan C., Avapa Chantasartrassmee, Saad I. El-Zanati, and Charles Vanden Eynden. "On Cyclic Decompositions of Complete Graphs into Tripartite Graphs." Journal of Graph Theory 72, no. 1 (2012): 90–111. http://dx.doi.org/10.1002/jgt.21632.

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9

Le, Xuan Hung. "Uniquely list colorability of complete tripartite graphs." Chebyshevskii sbornik 23, no. 2 (2022): 170–78. http://dx.doi.org/10.22405/2226-8383-2022-23-2-170-178.

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10

Rajasekaran, G., and R. Sampathkumar. "Optimal orientations of some complete tripartite graphs." Filomat 29, no. 8 (2015): 1681–87. http://dx.doi.org/10.2298/fil1508681r.

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For a graph G, let D(G) be the set of all strong orientations of G. The orientation number of G is d?(G) = min{d(D)|D ? D(G)},where d(D) denotes the diameter of the digraph D. In this paper, we determine the orientation number for some complete tripartite graphs.

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11

Kim, Suh-Ryung, and Yoshio Sano. "The competition numbers of complete tripartite graphs." Discrete Applied Mathematics 156, no. 18 (2008): 3522–24. http://dx.doi.org/10.1016/j.dam.2008.04.009.

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12

Chia, G. L., and Chee-Kit Ho. "Chromatic equivalence classes of complete tripartite graphs." Discrete Mathematics 309, no. 1 (2009): 134–43. http://dx.doi.org/10.1016/j.disc.2007.12.059.

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13

Ellingham, M. N., Chris Stephens, and Xiaoya Zha. "The nonorientable genus of complete tripartite graphs." Journal of Combinatorial Theory, Series B 96, no. 4 (2006): 529–59. http://dx.doi.org/10.1016/j.jctb.2005.10.004.

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14

Lau, G. C., and Y. H. Peng. "Chromatic uniqueness of certain complete tripartite graphs." Acta Mathematica Sinica, English Series 27, no. 5 (2011): 919–26. http://dx.doi.org/10.1007/s10114-011-8507-2.

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15

Grannell, M. J., and M. Knor. "On the number of triangular embeddings of complete graphs and complete tripartite graphs." Journal of Graph Theory 69, no. 4 (2011): 370–82. http://dx.doi.org/10.1002/jgt.20590.

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16

Gein, Pavel A. "ON CHROMATIC UNIQUENESS OF SOME COMPLETE TRIPARTITE GRAPHS." Ural Mathematical Journal 7, no. 1 (2021): 38. http://dx.doi.org/10.15826/umj.2021.1.004.

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Let \(P(G, x)\) be a chromatic polynomial of a graph \(G\). Two graphs \(G\) and \(H\) are called chromatically equivalent iff \(P(G, x) = H(G, x)\). A graph \(G\) is called chromatically unique if \(G\simeq H\) for every \(H\) chromatically equivalent to \(G\). In this paper, the chromatic uniqueness of complete tripartite graphs \(K(n_1, n_2, n_3)\) is proved for \(n_1 \geqslant n_2 \geqslant n_3 \geqslant 2\) and \(n_1 - n_3 \leqslant 5\).

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17

Grannell, M. J., and M. Knor. "Dihedral Biembeddings and Triangulations by Complete and Complete Tripartite Graphs." Graphs and Combinatorics 29, no. 4 (2012): 921–32. http://dx.doi.org/10.1007/s00373-012-1163-1.

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18

T., Arputha Jose, Sampath Kumar S., and Cecily Sahai C. "Decomposition of Complete Tripartite Graphs into Short Cycles." Ars Combinatoria 160, no. 1 (2024): 85–103. http://dx.doi.org/10.61091/ars-160-09.

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For a graph G and for non-negative integers p , q and r , the triplet ( p , q , r ) is said to be an admissible triplet, if 3 p + 4 q + 6 r = | E ( G ) | . If G admits a decomposition into p cycles of length 3 , q cycles of length 4 , and r cycles of length 6 for every admissible triplet ( p , q , r ) , then we say that G has a { C p 3 , C q 4 , C r 6 } -decomposition. In this paper, the necessary conditions for the existence of { C p 3 , C q 4 , C r 6 } -decomposition of K ℓ , m , n ( ℓ ≤ m ≤ n ) are proved to be sufficient. This affirmatively answers the problem raised in \emph{Decomposing complete tripartite graphs into cycles of lengths 3 and 4 , Discrete Math. 197/198 (1999), 123-135}. As a corollary, we deduce the main results of \emph{Decomposing complete tripartite graphs into cycles of lengths 3 and 4 , Discrete Math., 197/198, 123-135 (1999)} and \emph{Decompositions of complete tripartite graphs into cycles of lengths 3 and 6 , Austral. J. Combin., 73(1), 220-241 (2019)}.

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19

Varghese, Joseph, and A. Antonysamy. "On the Continuous Monotonic Decomposition of Some Complete Tripartite Graphs." Mapana - Journal of Sciences 8, no. 2 (2009): 7–19. http://dx.doi.org/10.12723/mjs.15.2.

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20

Bezegová, L'udmila, and Jaroslav Ivančo. "A characterization of complete tripartite degree-magic graphs." Discussiones Mathematicae Graph Theory 32, no. 2 (2012): 243. http://dx.doi.org/10.7151/dmgt.1608.

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21

Jin, Zemin, Shili Wen, and Shujun Zhou. "Heterochromatic tree partition problem in complete tripartite graphs." Discrete Mathematics 312, no. 4 (2012): 789–802. http://dx.doi.org/10.1016/j.disc.2011.11.005.

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22

Ellingham, M. N., and Justin Z. Schroeder. "Nonorientable hamilton cycle embeddings of complete tripartite graphs." Discrete Mathematics 312, no. 11 (2012): 1911–17. http://dx.doi.org/10.1016/j.disc.2012.02.012.

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23

Grannell, M. J., T. S. Griggs, M. Knor, and J. Širáň. "Triangulations of orientable surfaces by complete tripartite graphs." Discrete Mathematics 306, no. 6 (2006): 600–606. http://dx.doi.org/10.1016/j.disc.2005.10.025.

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24

Guo, Zhiwei, Haixing Zhao, and Yaping Mao. "The equitable vertex arboricity of complete tripartite graphs." Information Processing Letters 115, no. 12 (2015): 977–82. http://dx.doi.org/10.1016/j.ipl.2015.06.016.

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25

Alawn, Nawras A., Nadia M. G. Al-Saidi, and Rashed T. Rasheed. "Tripartite graphs with energy aggregation." Boletim da Sociedade Paranaense de Matemática 38, no. 7 (2019): 149–67. http://dx.doi.org/10.5269/bspm.v38i7.44463.

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The aggregate of the absolute values of the graph eigenvalues is called the energy of a graph. It is used to approximate the total _-electron energy of molecules. Thus, finding a new mechanism to calculate the total energy of some graphs is a challenge; it has received a lot of research attention. We study the eigenvalues of a complete tripartite graph Ti,i,n−2i , for n _ 4, based on the adjacency, Laplacian, and signless Laplacian matrices. In terms of the degree sequence, the extreme eigenvalues of the irregular graphs energy are found to characterize the component with the maximum energy. The chemical HMO approach is particularly successful in the case of the total _-electron energy. We showed that some chemical components are equienergetic with the tripartite graph. This discovering helps easily to derive the HMO for most of these components despite their different structures.

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26

Guo, Zhiwei, Haixing Zhao, and Yaping Mao. "On the equitable vertex arboricity of complete tripartite graphs." Discrete Mathematics, Algorithms and Applications 07, no. 04 (2015): 1550056. http://dx.doi.org/10.1142/s1793830915500561.

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The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu et al. introduced the concept of equitable [Formula: see text]-tree-coloring, which can be viewed as a generalization of proper equitable [Formula: see text]-coloring. The strong equitable vertex [Formula: see text]-arboricity of complete bipartite equipartition graphs was investigated in 2013. In this paper, we study the strong equitable vertex [Formula: see text]-arboricity of complete equipartition tripartite graphs. For most cases, the exact values of [Formula: see text] are obtained.

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27

Gethner, Ellen, Leslie Hogben, Bernard Lidický, Florian Pfender, Amanda Ruiz, and Michael Young. "On Crossing Numbers of Complete Tripartite and Balanced Complete Multipartite Graphs." Journal of Graph Theory 84, no. 4 (2016): 552–65. http://dx.doi.org/10.1002/jgt.22041.

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28

Varghese, Joseph, and A. Antonysamy. "On Some Complete Tripartite Graphs that Decline Continuous Monotonic Decomposition." Asian Journal of Engineering and Applied Technology 1, no. 1 (2012): 1–7. http://dx.doi.org/10.51983/ajeat-2012.1.1.2508.

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A collection of complete tripartite graphs, viz., K1,3,m, K2,3m, K2,5m and K3,5,m do not accept Continuous Monotonic Decomposition(CMD). It is shown that by an addition or removal of a single edge will make these graphs accept CMD. Eventually, the discussion helps to find a series of numbers which are not triangular.

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29

Hu, Si-wei, and Yi-chao Chen. "The Thickness of Some Complete Bipartite and Tripartite Graphs." Acta Mathematicae Applicatae Sinica, English Series 40, no. 4 (2024): 1001–14. http://dx.doi.org/10.1007/s10255-024-1128-1.

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30

Cavenagh, N. J. "Further decompositions of complete tripartite graphs into 5-cycles." Discrete Mathematics 256, no. 1-2 (2002): 55–81. http://dx.doi.org/10.1016/s0012-365x(01)00462-9.

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31

Billington, Elizabeth J., and D. G. Hoffman. "Decomposition of complete tripartite graphs into gregarious 4-cycles." Discrete Mathematics 261, no. 1-3 (2003): 87–111. http://dx.doi.org/10.1016/s0012-365x(02)00462-4.

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32

Wagner, Brian C. "Ascending Subgraph Decompositions in Oriented Complete Balanced Tripartite Graphs." Graphs and Combinatorics 29, no. 5 (2012): 1549–55. http://dx.doi.org/10.1007/s00373-012-1208-5.

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33

Kawarabayashi, Ken-ichi, Chris Stephens, and Xiaoya Zha. "Orientable and Nonorientable Genera for Some Complete Tripartite Graphs." SIAM Journal on Discrete Mathematics 18, no. 3 (2004): 479–87. http://dx.doi.org/10.1137/s0895480103429319.

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34

Petrosyan, T., and A. Drambyan. "VERTEX-DISTINGUISHING EDGE COLORINGS OF SOME COMPLETE TRIPARTITE GRAPHS." Herald of Russian-Armenian (Slavonic) University humanities and social sciences, no. 2 (2022): 7–18. http://dx.doi.org/10.48200/1829-0450_pmn_2022_2_7.

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35

Burger, AP, and JH van Vuuren. "The Irredundance-related Ramsey Numbers \(s(3,8)=21\) and \(w(3,8)=21\)." Utilitas Mathematica 120, no. 1 (2024): 93–107. http://dx.doi.org/10.61091/um120-08.

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For a graph G and for non-negative integers p, q, and r, the triplet \((p, q, r)\) is said to be an admissible triplet if \(3p + 4q + 6r = |E(G)|\). If G admits a decomposition into p cycles of length 3, q cycles of length 4, and r cycles of length 6 for every admissible triplet \((p, q, r)\), then we say that G has a \(\{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\}\)-decomposition. In this paper, the necessary conditions for the existence of \(\{C_{3}^{p}, C_{4}^{q}, C_{6}^{r}\}\)-decomposition of \(K_{\ell, m, n} (\ell \leq m \leq n)\) are proved to be sufficient. This affirmatively answers the problem raised in Decomposing complete tripartite graphs into cycles of lengths 3 and 4, Discrete Math. 197/198 (1999), 123-135. As a corollary, we deduce the main results of Decomposing complete tripartite graphs into cycles of lengths 3 and 4, Discrete Math., 197/198, 123-135 (1999) and Decompositions of complete tripartite graphs into cycles of lengths 3 and 6, Austral. J. Combin., 73(1), 220-241 (2019).

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36

Ellingham, M. N., Chris Stephens, and Xiaoya Zha. "Counterexamples to the nonorientable genus conjecture for complete tripartite graphs." European Journal of Combinatorics 26, no. 3-4 (2005): 387–99. http://dx.doi.org/10.1016/j.ejc.2004.01.009.

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37

Billington, Elizabeth J., and Nicholas J. Cavenagh. "Decomposing complete tripartite graphs into closed trails of arbitrary lengths." Czechoslovak Mathematical Journal 57, no. 2 (2007): 523–51. http://dx.doi.org/10.1007/s10587-007-0096-y.

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38

Liu, Ruying, Haixing Zhao, and Chengfu Ye. "A complete solution to a conjecture on chromatic uniqueness of complete tripartite graphs." Discrete Mathematics 289, no. 1-3 (2004): 175–79. http://dx.doi.org/10.1016/j.disc.2004.07.014.

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39

Grannell, M. J., and T. S. Griggs. "A lower bound for the number of triangular embeddings of some complete graphs and complete regular tripartite graphs." Journal of Combinatorial Theory, Series B 98, no. 4 (2008): 637–50. http://dx.doi.org/10.1016/j.jctb.2007.10.002.

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40

Staš, Michal, and Mária Timková. "On the Problems of CF-Connected Graphs for Kl,m,n." Mathematics 12, no. 13 (2024): 2068. http://dx.doi.org/10.3390/math12132068.

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A connected graph, G, is Crossing Free-connected (CF-connected) if there is a path between every pair of vertices with no crossing on its edges for each optimal drawing of G. We conjecture that a complete tripartite graph, Kl,m,n, is CF-connected if and only if it does not contain any of the following as a subgraph: K1,2,7, K1,3,5, K1,4,4, K2,2,5, K3,3,3. We examine the idea that K1,2,7, K1,3,5, K1,4,4, and K2,2,5 are the first non-CF-connected complete tripartite graphs. The CF-connectedness of Kl,m,n with l,m,n≥3 is dependent on the knowledge of crossing numbers of K3,3,n. In this paper, we prove various results that support this conjecture.

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41

Fronček, Dalibor. "Self-complementary factors of almost complete tripartite graphs of even order." Discrete Mathematics 236, no. 1-3 (2001): 111–22. http://dx.doi.org/10.1016/s0012-365x(00)00435-0.

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42

Billington, E. "Decomposing complete tripartite graphs into cycles of lengths 3 and 4." Discrete Mathematics 197-198, no. 1-3 (1999): 123–35. http://dx.doi.org/10.1016/s0012-365x(98)00227-1.

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43

Billington, Elizabeth J. "Decomposing complete tripartite graphs into cycles of lengths 3 and 4." Discrete Mathematics 197-198 (February 1999): 123–35. http://dx.doi.org/10.1016/s0012-365x(99)90049-3.

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44

Zhao, Hongtao, and C. A. Rodger. "Large sets of wrapped Hamilton cycle decompositions of complete tripartite graphs." Discrete Mathematics 338, no. 8 (2015): 1407–15. http://dx.doi.org/10.1016/j.disc.2015.03.005.

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45

Jing, Puning, Zhengke Miao, and Zi-Xia Song. "Some remarks on interval colorings of complete tripartite and biregular graphs." Discrete Applied Mathematics 277 (April 2020): 193–97. http://dx.doi.org/10.1016/j.dam.2019.08.024.

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46

Wang, Pi, Shasha Li, and Xiaoxue Gao. "k-Path-Connectivity of Completely Balanced Tripartite Graphs." Axioms 11, no. 6 (2022): 270. http://dx.doi.org/10.3390/axioms11060270.

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For a graph G=(V,E) and a set S⊆V(G) of a size at least 2, a path in G is said to be an S-path if it connects all vertices of S. Two S-paths P1 and P2 are said to be internally disjoint if E(P1)∩E(P2)=∅ and V(P1)∩V(P2)=S; that is, they share no vertices and edges apart from S. Let πG(S) denote the maximum number of internally disjoint S-paths in G. The k-path-connectivity πk(G) of G is then defined as the minimum πG(S), where S ranges over all k-subsets of V(G). In this paper, we study the k-path-connectivity of the complete balanced tripartite graph Kn,n,n and obtain πkKn,n,n=2nk−1 for 3≤k≤n.

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47

C., Sujatha, and Manickam A. "Continuous Monotonic Decomposition of Some Standard Graphs by using an Algorithm." International Journal of Basic Sciences and Applied Computing (IJBSAC) 2, no. 8 (2019): 6–9. https://doi.org/10.35940/ijbsac.H0103.072819.

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In this paper we elaborate an algorithm to compute the necessary and sufficient conditions for the continuous monotonic star decomposition of the bipartite graph Km,r and the number of vertices and the number of disjoint sets. Also an algorithm to find the tensor product of Pn  Ps has continuous monotonic path decomposition. Finally we conclude that in this paper the results described above are complete bipartite graphs that accept Continuous monotonic star decomposition. There are many other classes of complete tripartite graphs that accept Continuous monotonic star decomposition. In this research article Extended to complete m-partite graphs for grater values of m. Also the algorithm can be developed for the tensor product of different classes such as Cn Wn K1,n , , with Pn

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48

Priyadarsini, Shanmugasundaram, and Appu Muthusamy. "Decomposition of complete tripartite graphs into cycles and paths of length three." Contributions to Discrete Mathematics 15, no. 3 (2020): 117–29. http://dx.doi.org/10.55016/ojs/cdm.v15i3.62692.

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Let $C_{k}$ and $P_{k}$ denote a cycle and a path on $k$ vertices, respectively. In this paper, we obtain necessary and sufficient conditions for the decomposition of $K_{{r},{s},{t}}$ into $p$ copies of $C_{3}$ and $q$ copies of $P_{4}$ for all possible values of $p$, $q\geq0$.

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49

Nakprasit, Keaitsuda Maneeruk, and Kittikorn Nakprasit. "The strong equitable vertex 2-arboricity of complete bipartite and tripartite graphs." Information Processing Letters 117 (January 2017): 40–44. http://dx.doi.org/10.1016/j.ipl.2016.08.007.

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50

Ellingham, M. N., and Justin Z. Schroeder. "Orientable Hamilton Cycle Embeddings of Complete Tripartite Graphs I: Latin Square Constructions." Journal of Combinatorial Designs 22, no. 2 (2013): 71–94. http://dx.doi.org/10.1002/jcd.21375.

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