On Chordal-$k$-Generalized Split Graphs

Abstract

A graph $G$ is a {\em chordal-$k$-generalized split graph} if $G$ is chordal and there is a clique $Q$ in $G$ such that every connected component in $G[V\setminus Q]$ has at most $k$ vertices. Thus, chordal-$1$-generalized split graphs are exactly the split graphs. We characterize chordal-$k$-generalized split graphs by forbidden induced subgraphs. Moreover, we characterize a very special case of chordal-$2$-generalized split graphs for which the Efficient Domination problem is \NP-complete.

arXiv admin note: text overlap with arXiv:1701.03414

References in corpus (2)

• On Efficient Domination for Some Classes of $H$-Free Chordal Graphs
• Recognition of unipolar and generalised split graphs