Properly colored cycles in edge-colored graphs

Li, Ruonan

doi:10.3990/1.9789036544719

Cited by 2 publications

(2 citation statements)

References 47 publications

(108 reference statements)

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“…By the proofs of Observations 1.2 and 3.3 in [14] and [6], respectively, we know that if C is a PC cycle in a colored complete graph (complete bipartite graph), then each vertex of C is contained in a PC cycle of length 3 or 4 (4 or 6). In fact, by a similar argument, we can prove that if C is a PC cycle in a colored complete multipartite graph, then each vertex of C is contained in a PC cycle of length ∈ {3, 4, 6} (see Observation 1.9 in [13] Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.…”

Section: Algorithm 1 Construction Of H 0 H 1 H Smentioning

confidence: 92%

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Broersma

Zhang

2018

Graphs and Combinatorics

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With respect to specific cycle-related problems, edge-colored graphs can be considered as a generalization of directed graphs. We show that properly edge-colored theta graphs play a key role in characterizing the difference between edge-colored complete graphs and multipartite tournaments. We also establish sufficient conditions for an edgecolored complete graph to contain a small and a large properly edge-colored theta graph, respectively. Keywords Edge-colored graph • Complete graph • Properly edge-colored cycle • Properly edge-colored theta graph • Multipartite tournament Mathematics Subject Classification 05C15 • 05C20 • 05C38 Supported by CSC (No. 201506290097) and NSFC (No. 11671320).

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Section: Algorithm 1 Construction Of H 0 H 1 H Smentioning

confidence: 92%

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Broersma

Zhang

2018

Graphs and Combinatorics

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“…In fact, Bermond-Thomassen's conjecture has not even been confirmed in multi-partite tournaments. Recently, Li et al [7] revealed a relationship between PC cycles in edgecolored complete graphs and Bermond-Thomassen's conjecture on multi-partite tournaments.…”

Section: For Each Vertex I ∈ V(g) For Each Vertex I ∈ a The Bad Ementioning

confidence: 99%

Decomposing edge-colored graphs under color degree constraints

Fujita

Wang

2017

Electronic Notes in Discrete Mathematics

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For an edge-colored graph G, the minimum color degree of G means the minimum number of colors on edges which are adjacent to each vertex of G. We prove that if G is an edge-colored graph with minimum color degree at least 5 then V(G) can be partitioned into two parts such that each part induces a subgraph with minimum color degree at least 2. We show this theorem by proving a much stronger form. Moreover, we point out an important relationship between our theorem and Bermond-Thomassen's conjecture in digraphs.

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Properly colored cycles in edge-colored graphs

Cited by 2 publications

References 47 publications

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Properly Edge-colored Theta Graphs in Edge-colored Complete Graphs

Decomposing edge-colored graphs under color degree constraints

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