Discrete Mathematics ( IF 0.770 ) Pub Date : 2020-01-31 , DOI: 10.1016/j.disc.2020.111825 Deborah Oliveros; Christopher O’Neill; Shira Zerbib
An -segment hypergraph is a hypergraph whose edges consist of consecutive integer points on line segments in . In this paper, we bound the chromatic number and covering number of hypergraphs in this family, uncovering several interesting geometric properties in the process. We conjecture that for , the covering number is at most , where denotes the matching number of . We prove our conjecture in the case where , and provide improved (in fact, optimal) bounds on for . We also provide sharp bounds on the chromatic number in terms of , and use them to prove two fractional versions of our conjecture.