Veto Interval Graphs and Variations [article]

Breeann Flesch, Jessica Kawana, Joshua D. Laison, Dana Lapides, Stephanie Partlow, Gregory J. Puleo
2018 arXiv   pre-print
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 ab is in the graph if the intervals corresponding to the vertices a and b 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
more » ... eral 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.
arXiv:1709.09259v2 fatcat:5h2zjm5vyfggngsvy2uky7bpke