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Relevant bibliographies by topics / Rainbow subgraph

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Journal articles

Academic literature on the topic 'Rainbow subgraph'

Author: Grafiati

Published: 25 May 2024

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Journal articles on the topic "Rainbow subgraph"

1

Axenovich, Maria, Tao Jiang, and Z. Tuza. "Local Anti-Ramsey Numbers of Graphs." Combinatorics, Probability and Computing 12, no. 5-6 (2003): 495–511. http://dx.doi.org/10.1017/s0963548303005868.

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A subgraph H in an edge-colouring is properly coloured if incident edges of H are assigned different colours, and H is rainbow if no two edges of H are assigned the same colour. We study properly coloured subgraphs and rainbow subgraphs forced in edge-colourings of complete graphs in which each vertex is incident to a large number of colours.

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2

Lestari, Dia, and I. Ketut Budayasa. "BILANGAN KETERHUBUNGAN PELANGI PADA PEWARNAAN-SISI GRAF." MATHunesa: Jurnal Ilmiah Matematika 8, no. 1 (2020): 25–34. http://dx.doi.org/10.26740/mathunesa.v8n1.p25-34.

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Let be a graph. An edge-coloring of is a function , where is a set of colors. Respect to a subgraph of is called a rainbow subgraph if all edges of get different colors. Graph is called rainbow connected if for every two distinct vertices of is joined by a rainbow path. The rainbow connection number of , denoted by , is the minimum number of colors needed in coloring all edges of such that is a rainbow connected. The main problem considered in this thesis is determining the rainbow connection number of graph. In this thesis, we determine the exact value of the rainbow connection number of some

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3

KOSTOCHKA, ALEXANDR, and MATTHEW YANCEY. "Large Rainbow Matchings in Edge-Coloured Graphs." Combinatorics, Probability and Computing 21, no. 1-2 (2012): 255–63. http://dx.doi.org/10.1017/s0963548311000605.

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Arainbow subgraphof an edge-coloured graph is a subgraph whose edges have distinct colours. Thecolour degreeof a vertexvis the number of different colours on edges incident withv. Wang and Li conjectured that fork≥ 4, every edge-coloured graph with minimum colour degreekcontains a rainbow matching of size at least ⌈k/2⌉. A properly edge-colouredK4has no such matching, which motivates the restrictionk≥ 4, but Li and Xu proved the conjecture for all other properly coloured complete graphs. LeSaulnier, Stocker, Wenger and West showed that a rainbow matching of size ⌊k/2⌋ is guaranteed to exist, a

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4

Hüffner, Falk, Christian Komusiewicz, Rolf Niedermeier, and Martin Rötzschke. "The Parameterized Complexity of the Rainbow Subgraph Problem." Algorithms 8, no. 1 (2015): 60–81. http://dx.doi.org/10.3390/a8010060.

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5

Matos Camacho, Stephan, Ingo Schiermeyer, and Zsolt Tuza. "Approximation algorithms for the minimum rainbow subgraph problem." Discrete Mathematics 310, no. 20 (2010): 2666–70. http://dx.doi.org/10.1016/j.disc.2010.03.032.

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6

Koch, Maria, Stephan Matos Camacho, and Ingo Schiermeyer. "Algorithmic approaches for the minimum rainbow subgraph problem." Electronic Notes in Discrete Mathematics 38 (December 2011): 765–70. http://dx.doi.org/10.1016/j.endm.2011.10.028.

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7

Gyárfás, András, Jenő Lehel, and Richard H. Schelp. "Finding a monochromatic subgraph or a rainbow path." Journal of Graph Theory 54, no. 1 (2006): 1–12. http://dx.doi.org/10.1002/jgt.20179.

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8

LOH, PO-SHEN, and BENNY SUDAKOV. "Constrained Ramsey Numbers." Combinatorics, Probability and Computing 18, no. 1-2 (2009): 247–58. http://dx.doi.org/10.1017/s0963548307008875.

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For two graphs S and T, the constrained Ramsey number f(S, T) is the minimum n such that every edge colouring of the complete graph on n vertices (with any number of colours) has a monochromatic subgraph isomorphic to S or a rainbow subgraph isomorphic to T. Here, a subgraph is said to be rainbow if all of its edges have different colours. It is an immediate consequence of the Erdős–Rado Canonical Ramsey Theorem that f(S, T) exists if and only if S is a star or T is acyclic. Much work has been done to determine the rate of growth of f(S, T) for various types of parameters. When S and T are bot

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9

Schiermeyer, Ingo. "On the minimum rainbow subgraph number of a graph." Ars Mathematica Contemporanea 6, no. 1 (2012): 83–88. http://dx.doi.org/10.26493/1855-3974.246.94d.

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10

Katrenič, Ján, and Ingo Schiermeyer. "Improved approximation bounds for the minimum rainbow subgraph problem." Information Processing Letters 111, no. 3 (2011): 110–14. http://dx.doi.org/10.1016/j.ipl.2010.11.005.

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