Equimatchable Claw-Free Graphs
Saieed Akbari, Hadi Alizadeh, T{\i}naz Ekim, Didem G\"oz\"upek,, Mordechai Shalom
TL;DR
This paper characterizes claw-free equimatchable graphs, providing a foundational understanding and an efficient recognition algorithm for these special graph classes.
Contribution
It offers the first characterization of claw-free equimatchable graphs by identifying their specific graph families.
Findings
First characterization of claw-free equimatchable graphs
Identification of specific graph families within this class
Development of an efficient recognition algorithm
Abstract
A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide, to the best of our knowledge, the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.
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