Properly colored and rainbow C 4 ${C}_{4}$ 's in edge-colored graphs

IF 0.9 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2023-08-09 DOI:10.1002/jgt.23019

Fangfang Wu, Hajo Broersma, Shenggui Zhang, Binlong Li

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引用次数: 0

Abstract

We present new sharp sufficient conditions for the existence of properly colored and rainbow $C_{4}$ 's in edge-colored graphs. Our first results deal with sharp color neighborhood conditions for the existence of properly colored $C_{4}$ 's in edge-colored complete graphs and complete bipartite graphs, respectively. Next, we characterize the extremal graphs for an anti-Ramsey number result due to Alon on the existence of rainbow $C_{4}$ 's in edge-colored complete graphs. We also generalize Alon's result from complete to general edge-colored graphs. Finally, we derive a structural property regarding the extremal graphs for a bipartite counterpart of Alon's result due to Axenovich, Jiang, and Kündgen on the existence of rainbow $C_{4}$ 's in edge-colored complete bipartite graphs. We also generalize their result from complete to general bipartite edge-colored graphs.

Abstract Image

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颜色合适，彩虹C4${C}_{4} 边色图中的$

我们给出了边着色图中存在适当着色和彩虹的新的充分条件。我们的第一个结果分别处理了边色完全图和完全二部图中正确着色的存在的尖锐色邻域条件。接下来，我们刻画了由Alon引起的反Ramsey数结果的极值图关于边色完全图中彩虹的存在性。我们还将Alon的结果从完全图推广到一般的边色图。最后，我们导出了关于二分图的极值图的一个结构性质，该极值图是由Axenovich、Jiang和Kündgen关于边色完全二分图中彩虹的存在性的Alon结果的对应物。我们还将他们的结果从完全图推广到一般的二分边色图。

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .