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arXiv · 1709.09259

Veto Interval Graphs and Variations

Breeann Flesch·Jessica Kawana·Joshua D. Laison·Dana Lapides·Stephanie Partlow·Gregory J. Puleo
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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 $ab$ 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 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.

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Breeann Flesch, Jessica Kawana, Joshua D. Laison, Dana Lapides, Stephanie Partlow, Gregory J. Puleo. 2018-07-26. Veto Interval Graphs and Variations. https://arxiv.org/abs/1709.09259

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