On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs
Xiao-Chuan Liu, Xu Yang

TL;DR
This paper investigates color isomorphic pairs in proper edge colorings of complete graphs, providing new upper and lower bounds for specific graph families using probabilistic methods.
Contribution
It introduces bounds for color isomorphism problems in complete graphs for certain graph families, extending previous work with new probabilistic techniques.
Findings
Upper bounds for $f_2(n,H)$ for certain rooted power graphs.
Matching lower bounds for 1-subdivisions of complete bipartite graphs.
Application of the random polynomial method of Bukh.
Abstract
Following the recent paper which initiated the study of colour isomorphism problems for complete graphs, we obtain upper bounds for for a family of graphs obtained as the -th rooted power of a balanced rooted tree for some sufficiently large . The proof uses the random polynomial method of Bukh. We also obtain matching lower bounds for -subdivisions of the complete bipartite graph.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Graph theory and applications
