Veto Interval Graphs and Variations
Combinatorics
2018-07-30 v2
Abstract
We introduce a variation of interval graphs, called veto interval (VI) graphs. A VI graph is represented by a set of closed intervals, each containing a point called a veto mark. The edge is in the graph if the intervals corresponding to the vertices and intersect, and neither contains the veto mark of the other. We find families of graphs which are VI graphs, and prove results towards characterizing the maximum chromatic number of a VI graph. We define and prove similar results about several related graph families, including unit VI graphs, midpoint unit VI (MUVI) graphs, and single and double approval graphs. We also highlight a relationship between approval graphs and a family of tolerance graphs.
Keywords
Cite
@article{arxiv.1709.09259,
title = {Veto Interval Graphs and Variations},
author = {Breeann Flesch and Jessica Kawana and Joshua D. Laison and Dana Lapides and Stephanie Partlow and Gregory J. Puleo},
journal= {arXiv preprint arXiv:1709.09259},
year = {2018}
}