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Relevant bibliographies by topics / Edge-colored graph theory

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Journal articles

Academic literature on the topic 'Edge-colored graph theory'

Author: Grafiati

Published: 14 December 2024

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Journal articles on the topic "Edge-colored graph theory"

1

Ma, Huawen. "Maximum Colored Cuts in Edge-Colored Complete Graphs." Journal of Mathematics 2022 (July 7, 2022): 1–4. http://dx.doi.org/10.1155/2022/9515498.

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Max-Cut problem is one of the classical problems in graph theory and has been widely studied in recent years. Maximum colored cut problem is a more general problem, which is to find a bipartition of a given edge-colored graph maximizing the number of colors in edges going across the bipartition. In this work, we gave some lower bounds on maximum colored cuts in edge-colored complete graphs containing no rainbow triangles or properly colored 4-cycles.

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2

Guo, Zhiwei, Hajo Broersma, Ruonan Li, and Shenggui Zhang. "Some algorithmic results for finding compatible spanning circuits in edge-colored graphs." Journal of Combinatorial Optimization 40, no. 4 (2020): 1008–19. http://dx.doi.org/10.1007/s10878-020-00644-7.

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Abstract A compatible spanning circuit in a (not necessarily properly) edge-colored graph G is a closed trail containing all vertices of G in which any two consecutively traversed edges have distinct colors. Sufficient conditions for the existence of extremal compatible spanning circuits (i.e., compatible Hamilton cycles and Euler tours), and polynomial-time algorithms for finding compatible Euler tours have been considered in previous literature. More recently, sufficient conditions for the existence of more general compatible spanning circuits in specific edge-colored graphs have been establ

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3

Razumovsky, P. V., and M. B. Abrosimov. "THE MINIMAL VERTEX EXTENSIONS FOR COLORED COMPLETE GRAPHS." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 4 (2021): 77–89. http://dx.doi.org/10.14529/mmph210409.

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The article proposes the results of the search for minimal vertex extensions of undirected colored complete graphs. The research topic is related to the modelling of full fault tolerant technical systems with a different type of their objects in the terminology of graph theory. Let a technical system be Σ, then there is a graph G(Σ), which vertices reflects system’s objects and edges reflects connections between these objects. Type of each object reflected in a mapping of some color from F = {1,2…,i} to the corresponding vertex. System’s Σ vertex extension is a graph G(Σ) which contains additi

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4

Wang, Yiqiao, Juan Liu, Yongtang Shi, and Weifan Wang. "Star Chromatic Index of 1-Planar Graphs." Symmetry 14, no. 6 (2022): 1177. http://dx.doi.org/10.3390/sym14061177.

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Many symmetric properties are well-explored in graph theory, especially in graph coloring, such as symmetric graphs defined by the automorphism groups, symmetric drawing of planar graphs, and symmetric functions which are used to count the number of specific colorings of a graph. This paper is devoted to studying the star edge coloring of 1-planar graphs. The star chromatic index χst′(G) of a graph G is defined as the smallest k for which the edges of G can be colored by using k colors so that no two adjacent edges get the same color and no bichromatic paths or cycles of length four are produc

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5

Yin, Huixin, Miaomiao Han, and Murong Xu. "Strong Edge Coloring of K4(t)-Minor Free Graphs." Axioms 12, no. 6 (2023): 556. http://dx.doi.org/10.3390/axioms12060556.

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A strong edge coloring of a graph G is a proper coloring of edges in G such that any two edges of distance at most 2 are colored with distinct colors. The strong chromatic index χs′(G) is the smallest integer l such that G admits a strong edge coloring using l colors. A K4(t)-minor free graph is a graph that does not contain K4(t) as a contraction subgraph, where K4(t) is obtained from a K4 by subdividing edges exactly t−4 times. The paper shows that every K4(t)-minor free graph with maximum degree Δ(G) has χs′(G)≤(t−1)Δ(G) for t∈{5,6,7} which generalizes some known results on K4-minor free gr

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6

DINITZ, YEFIM, MATTHEW J. KATZ, and ROI KRAKOVSKI. "GUARDING RECTANGULAR PARTITIONS." International Journal of Computational Geometry & Applications 19, no. 06 (2009): 579–94. http://dx.doi.org/10.1142/s0218195909003131.

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A rectangular partition is a partition of a rectangle into non-overlapping rectangles, such that no four rectangles meet at a common point. A vertex guard is a guard located at a vertex of the partition (i.e., at a corner of a rectangle); it guards the rectangles that meet at this vertex. An edge guard is a guard that patrols along an edge of the partition, and is thus equivalent to two adjacent vertex guards. We consider the problem of finding a minimum-cardinality guarding set for the rectangles of the partition. For vertex guards, we prove that guarding a given subset of the rectangles is N

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7

Soulé, Antoine, Vladimir Reinharz, Roman Sarrazin-Gendron, Alain Denise, and Jérôme Waldispühl. "Finding recurrent RNA structural networks with fast maximal common subgraphs of edge-colored graphs." PLOS Computational Biology 17, no. 5 (2021): e1008990. http://dx.doi.org/10.1371/journal.pcbi.1008990.

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RNA tertiary structure is crucial to its many non-coding molecular functions. RNA architecture is shaped by its secondary structure composed of stems, stacked canonical base pairs, enclosing loops. While stems are precisely captured by free-energy models, loops composed of non-canonical base pairs are not. Nor are distant interactions linking together those secondary structure elements (SSEs). Databases of conserved 3D geometries (a.k.a. modules) not captured by energetic models are leveraged for structure prediction and design, but the computational complexity has limited their study to local

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8

Wicaksono, Pramitha Shafika, and Kartono Kartono. "ANALISIS PENJADWALAN MATA PELAJARAN MENGGUNAKAN ALGORITMA WELCH-POWELL." Prismatika: Jurnal Pendidikan dan Riset Matematika 3, no. 1 (2020): 1–21. http://dx.doi.org/10.33503/prismatika.v3i1.1008.

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At the beginning of each semester, subjects scheduling is always carried out by the curriculum representatives and academic staff. There were several problems that must be avoided in subjects scheduling, these problems were the schedule of teachers who teach one subject at the same time are scheduled in different classes, teachers who teach more than one subject are scheduled in the same class at the same time, teachers who are lack of scheduled for teaching. In the subject of graph theory, there is a concept of graph coloring, one of which is vertex coloring. In vertex coloring, there is a We

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9

Muranov, Yuri V., and Anna Szczepkowska. "Path homology theory of edge-colored graphs." Open Mathematics 19, no. 1 (2021): 706–23. http://dx.doi.org/10.1515/math-2021-0049.

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Abstract In this paper, we introduce the category and the homotopy category of edge-colored digraphs and construct the functorial homology theory on the foundation of the path homology theory provided by Grigoryan, Muranov, and Shing-Tung Yau. We give the construction of the path homology theory for edge-colored graphs that follows immediately from the consideration of natural functor from the category of graphs to the subcategory of symmetrical digraphs. We describe the natural filtration of path homology groups of any digraph equipped with edge coloring, provide the definition of the corresp

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10

Lamken, Esther R., and Richard M. Wilson. "Decompositions of Edge-Colored Complete Graphs." Journal of Combinatorial Theory, Series A 89, no. 2 (2000): 149–200. http://dx.doi.org/10.1006/jcta.1999.3005.

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