Affiliation:
1. Ferdowsi University of Mashhad
2. University of Zagreb
Abstract
Let $G=(V_G, E_G)$ be a simple and connected graph. A set $M\subseteq E_G$ is called a matching of
$G$ if no two edges of $M$ are adjacent. The number of edges in $M$ is called
its size. A matching $M$ is maximal if it cannot be extended to a larger
matching in $G$. The smallest size of a maximal matching is called the
saturation number of $G$. In this paper we are concerned with the saturation
numbers of lexicographic product of graphs. We also address and solve an open
problem about the size of maximum matchings in graphs with a given maximum
degree $\Delta$.
Subject
Geometry and Topology,Statistics and Probability,Algebra and Number Theory,Analysis
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