寻找平衡：分裂图和相关类
Finding Balance: Split Graphs and Related Classes
摘要：
一个图是分裂图，如果它的顶点集可以划分为一个团和一个独立集。一个分裂图是不平衡的，如果存在两个这样的分区是不同的。Cheng，Collins和Trenk（2016）发现了以下有趣的计数事实：$n$顶点上的未标记，不平衡分裂图可以放置到双射中，所有未标记分裂图都在$n-1$或更少的顶点上。在本文中，我们把这些概念和定理不同的组合设置：最小集覆盖，二部图与一个杰出的块和偏序集的高度1。
英文摘要：
A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following interesting counting fact: unlabeled, unbalanced split graphs on $n$ vertices can be placed into a bijection with all unlabeled split graphs on $n-1$ or fewer vertices. In this paper we translate these concepts and the theorem to different combinatorial settings: minimal set covers, bipartite graphs with a distinguished block and posets of height one.
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。
