English

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 abab is in the graph if the intervals corresponding to the vertices aa and bb 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}
}
R2 v1 2026-06-22T21:55:56.560Z