Rainbow Tur\'an Methods for Trees
Combinatorics
2022-03-28 v1
Abstract
The rainbow Tur\'an number, a natural extension of the well studied traditional Tur\'an number, was introduced in 2007 by Keevash, Mubayi, Sudakov and Verstra\"ete. The rainbow Tur\'an number of a graph , , is the largest number of edges for an vertex graph which can be properly edge colored with no rainbow subgraph. We explore the reduction method for finding upper bounds on rainbow Tur\'an numbers, and use this to inform results for the rainbow Tur\'an numbers of double stars, caterpillars, and perfect binary trees. In addition, we define -unique colorings and the related -unique Tur\'an numbers. We provide preliminary results on this new variant on the classic problem.
Keywords
Cite
@article{arxiv.2203.13765,
title = {Rainbow Tur\'an Methods for Trees},
author = {Vic Bednar and Neal Bushaw},
journal= {arXiv preprint arXiv:2203.13765},
year = {2022}
}