English

Two-coloring triples such that in each color class every element is missed at least once

Combinatorics 2020-08-24 v2

Abstract

We give a characterization of finite sets of triples of elements (e.g., positive integers) that can be colored with two colors such that for every element ii in each color class there exists a triple which does not contain ii. We give a linear (in the number of triples) time algorithm to decide if such a coloring exists and find one if it does. We also consider generalizations of this result and an application to a matching problem, which motivated this study. Finally, we show how these results translate to results about colorings of hypergraphs in which the degree of every vertex is kk less than the number of hyperedges.

Keywords

Cite

@article{arxiv.1910.02417,
  title  = {Two-coloring triples such that in each color class every element is missed at least once},
  author = {Balázs Keszegh},
  journal= {arXiv preprint arXiv:1910.02417},
  year   = {2020}
}