否决区间图及其变分
Veto Interval Graphs and Variations
摘要：
我们引入了区间图的一种变体，称为否决区间（VI）图。VI图由一组闭区间表示，每个区间包含一个称为否决标记的点。如果对应于顶点$a$和$b$的区间相交，并且都不包含另一个的否决标记，则边$ab$在图中。我们发现了一类图是VI图，并证明了刻画VI图的最大色数的结果。我们定义并证明了关于几个相关图族的类似结果，包括单元VI图、中点单元VI（MUVI）图以及单批准图和双批准图。我们还强调批准图和家庭的公差图之间的关系。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
