Complete bipartite graphs without small rainbow stars
Weizhen Chen, Meng Ji, Yaping Mao, Meiqin Wei

TL;DR
This paper investigates the structure of bipartite graphs avoiding small rainbow stars and determines exact Gallai-Ramsey numbers for certain bipartite graphs with respect to unions of cycles, paths, and stars.
Contribution
It provides a structural theorem for bipartite graphs without rainbow $K_{1,3}$ and calculates exact bipartite Gallai-Ramsey numbers for specific graph configurations.
Findings
Structural characterization of bipartite graphs without rainbow $K_{1,3}$
Exact Gallai-Ramsey numbers for $P_4$, $P_5$, and $K_{1,3}$ with unions of cycles, paths, and stars
Extensions of bipartite Gallai-Ramsey theory to new graph classes
Abstract
The -edge-colored bipartite Gallai-Ramsey number is defined as the minimum integer such that and for every , every edge-coloring (using all colors) of complete bipartite graph contains a rainbow copy of or a monochromatic copy of . In this paper, we first study the structural theorem on the complete bipartite graph with no rainbow copy of . Next, we utilize the results to prove the exact values of , , , where is a various union of cycles and paths and stars.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Topology and Set Theory · Advanced Graph Theory Research
