On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs
Combinatorics
2022-01-05 v1
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.
Keywords
Cite
@article{arxiv.2201.00838,
title = {On Color Isomorphic Pairs in Proper Edge Colourings of Complete Graphs},
author = {Xiao-Chuan Liu and Xu Yang},
journal= {arXiv preprint arXiv:2201.00838},
year = {2022}
}