Improved Bounds for Uniform Hypergraphs without Property B
Combinatorics
2019-12-10 v4
Abstract
A hypergraph is said to be properly 2-colorable if there exists a 2-coloring of its vertices such that no hyperedge is monochromatic. On the other hand, a hypergraph is called non-2-colorable if there exists at least one monochromatic hyperedge in each of the possible 2-colorings of its vertex set. Let m(n) denote the minimum number of hyperedges in a non-2-colorable n-uniform hypergraph. Establishing the lower and upper bounds on m(n) is a well-studied research direction over several decades. In this paper, we present new constructions for non-2-colorable n-uniform hypergraphs. These constructions improve the upper bounds for m(8), m(13), m(14), m(16) and m(17). We also improve the lower bound for m(5).
Cite
@article{arxiv.1602.00218,
title = {Improved Bounds for Uniform Hypergraphs without Property B},
author = {Sachin Aglave and V. A. Amarnath and Saswata Shannigrahi and Shwetank Singh},
journal= {arXiv preprint arXiv:1602.00218},
year = {2019}
}