On 2-colored graphs and partitions of boxes
Combinatorics
2018-10-23 v1 Discrete Mathematics
Abstract
We prove that if the edges of a graph G can be colored blue or red in such a way that every vertex belongs to a monochromatic k-clique of each color, then G has at least 4(k-1) vertices. This confirms a conjecture of Bucic, Lidicky, Long, and Wagner (arXiv:1805.11278[math.CO]) and thereby solves the 2-dimensional case of their problem about partitions of discrete boxes with the k-piercing property. We also characterize the case of equality in our result.
Keywords
Cite
@article{arxiv.1810.08920,
title = {On 2-colored graphs and partitions of boxes},
author = {Ron Holzman},
journal= {arXiv preprint arXiv:1810.08920},
year = {2018}
}
Comments
11 pages, 1 figure