Rainbow matchings in strongly edge-colored graphs

Babu, Jasine; Chandran, L. Sunil; Vaidyanathan, Krishna

doi:10.1016/j.disc.2014.12.019

Cited by 10 publications

(2 citation statements)

References 10 publications

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“…In 2015 Babu-Chandran-Vaidyanathan [1] showed that r(G) ≥ ⌊3δ(G)/4⌋ for any strongly edge-colored graph G with |V (G)| ≥ 2⌊3δ(G)/4⌋. They also proposed an interesting question: Is there a constant c greater than 3/4 such that every strongly edge-colored graph…”

Section: Introductionmentioning

confidence: 99%

Large rainbow matchings in edge-colored graphs with given average color degree

Zhou

2021

Preprint

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A rainbow matching in an edge-colored graph is a matching in which no two edges have the same color. The color degree of a vertex v is the number of different colors on edges incident to v. Kritschgau [Electron. J. Combin. 27(2020)] studied the existence of rainbow matchings in edge-colored graph G with average color degree at least 2k, and proved some sufficient conditions for a rainbow marching of size k in G. The sufficient conditions include that |V (G)| ≥ 12k 2 + 4k, or G is a properly edge-colored graph with |V (G)| ≥ 8k. In this paper, we show that every edge-colored graph G with |V (G)| ≥ 4k − 4 and average color degree at least 2k −1 contains a rainbow matching of size k. In addition, we also prove that every strongly edge-colored graph G with average degree at least 2k − 1 contains a rainbow matching of size at least k. The bound is sharp for complete graphs.

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Section: Introductionmentioning

confidence: 99%

Large rainbow matchings in edge-colored graphs with given average color degree

Zhou

2021

Preprint

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“…If the graph is properly edge-colored (i.e., no two adjacent edges have the same color), several results [11,12,13,14] have provided lower bounds for the size of a maximum rainbow matching. Other recent studies [15,16,17] have focused on finding large rainbow matchings under the stronger assumption that the given is strongly edge-colored. See Kano and Li [18] for a deeper analysis of rainbow subgraphs in an edge-colored graph.…”

Section: Introductionmentioning

confidence: 99%

Rainbow Perfect and Near-Perfect Matchings in Complete Graphs with Edges Colored by Circular Distance

Saito¹,

Wu²,

Matsumoto³

2020

Preprint

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Given an edge-colored complete graph K n on n vertices, a perfect (respectively, near-perfect) matching M in K n with an even (respectively, odd) number of vertices is rainbow if all edges have distinct colors. In this paper, we consider an edge coloring of K n by circular distance, and we denote the resulting complete graph by K • n . We show that when K • n has an even number of vertices, it contains a rainbow perfect matching if and only if n = 8k or n = 8k + 2, where k is a nonnegative integer. In the case of an odd number of vertices, Kirkman matching is known to be a rainbow near-perfect matching in K • n . However, real-world applications sometimes require multiple rainbow near-perfect matchings. We propose a method for using a recursive algorithm to generate multiple rainbow near-perfect matchings in K • n . KeywordsRainbow perfect matching • Edge-colored complete graph • Circular distance • Sports scheduling • Round-robin tournament . Kostochka and Yancey [9] completed a proof of Wang and Li's conjecture. Letting n be the size of vertices of a graph G, Lo [10] showed that an edge-colored graph G contains a rainbow matching of size at least k, where k = min δ(G), 2n−4 7

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Large Rainbow Matchings in Edge-Colored Graphs with Given Average Color Degree

Zhou

2022

Graphs and Combinatorics

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Rainbow matchings in strongly edge-colored graphs

Cited by 10 publications

References 10 publications

Large rainbow matchings in edge-colored graphs with given average color degree

Large rainbow matchings in edge-colored graphs with given average color degree

Rainbow Perfect and Near-Perfect Matchings in Complete Graphs with Edges Colored by Circular Distance

Large Rainbow Matchings in Edge-Colored Graphs with Given Average Color Degree

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