Efficient and Perfect domination on circular-arc graphs

Abstract

Given a graph $G=(V,E)$, a \emph{perfect dominating set} is a subset of vertices $V^{\prime }\subseteq V(G)$ such that each vertex $v\in V(G)\setminus V^{\prime }$ is dominated by exactly one vertex $v^{\prime }\in V^{\prime }$. An \emph{efficient dominating set} is a perfect dominating set $V^{\prime }$ where $V^{\prime }$ is also an independent set. These problems are usually posed in terms of edges instead of vertices. Both problems, either for the vertex or edge variant, remains NP-Hard, even when restricted to certain graphs families. We study both variants of the problems for the circular-arc graphs, and show efficient algorithms for all of them.

References in corpus (1)

• Exact algorithms for dominating induced matchings