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- Title
Properly colored and rainbow C4 ${C}_{4}$'s in edge‐colored graphs.
- Authors
Wu, Fangfang; Broersma, Hajo; Zhang, Shenggui; Li, Binlong
- Abstract
We present new sharp sufficient conditions for the existence of properly colored and rainbow C4 ${C}_{4}$'s in edge‐colored graphs. Our first results deal with sharp color neighborhood conditions for the existence of properly colored C4 ${C}_{4}$'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 C4 ${C}_{4}$'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 C4 ${C}_{4}$'s in edge‐colored complete bipartite graphs. We also generalize their result from complete to general bipartite edge‐colored graphs.
- Subjects
COMPLETE graphs; RAINBOWS; BIPARTITE graphs; RAMSEY numbers; COLOR
- Publication
Journal of Graph Theory, 2024, Vol 105, Issue 1, p110
- ISSN
0364-9024
- Publication type
Article
- DOI
10.1002/jgt.23019