English

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 f2(n,H)f_2(n,H) for a family of graphs HH obtained as the K0K_0-th rooted power of a balanced rooted tree for some sufficiently large K0K_0. The proof uses the random polynomial method of Bukh. We also obtain matching lower bounds for 11-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}
}