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Acta Mathematica Vietnamica

VERTEXSET CONTAINED IN LONGEST DOMINATING CYCLES IN GRAPHS

icon-email VU DINH HOA

Abstract

Let $G$ be an undirected and simple graph. A cycle $C$ in $G$ is called a {\it dominating cycle} if $V(G)-V(C)$ is an independent set of vertices in $G$. $G$ is called {\it dominable} if $G$ contains a dominating cycle $C$, and we say $G$ is {\it dominated} by $C$. In this paper we establish sets of vertices which are contained in any longest dominating cycle in $G$.