Karen L. Collins, Ann N. Trenk
Published 2017-06-09Version 1
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.
On Equistable, Split, CIS, and Related Classes of Graphs
Long paths and cycles in subgraphs of the cube
On homometric sets in graphs
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