On the number of $r$-matchings in a Tree

On the number of $r$-matchings in a Tree

An $r$-matching in a graph $G$ is a collection of edges in $G$ such that the distance between any two edges is at least $r$. A $2$-matching is also called an induced matching. In this paper, we estimate the maximum number of $r$-matchings in a tree of fixed order. We also prove that the $n$-vertex p...

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Hauptverfasser: Kang, Dong Yeap, Kim, Jaehoon, Kim, Younjin, Law, Hiu-Fai
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Combinatorics
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Zusammenfassung:An $r$-matching in a graph $G$ is a collection of edges in $G$ such that the distance between any two edges is at least $r$. A $2$-matching is also called an induced matching. In this paper, we estimate the maximum number of $r$-matchings in a tree of fixed order. We also prove that the $n$-vertex path has the maximum number of induced matchings among all $n$-vertex trees.
DOI:10.48550/arxiv.1409.7795