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arXiv · 2201.00838

On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs

Xiao-Chuan Liu·Xu Yang
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Abstract

Following the recent paper which initiated the study of colour isomorphism problems for complete graphs, we obtain upper bounds for $f_2(n,H)$ for a family of graphs $H$ obtained as the $K_0$-th rooted power of a balanced rooted tree for some sufficiently large $K_0$. The proof uses the random polynomial method of Bukh. We also obtain matching lower bounds for $1$-subdivisions of the complete bipartite graph.

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Xiao-Chuan Liu, Xu Yang. 2022-01-03. On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs. https://arxiv.org/abs/2201.00838

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