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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| creator | Kang, Dong Yeap Kim, Jaehoon Kim, Younjin Law, Hiu-Fai |
| description | 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_str_mv | 10.48550/arxiv.1409.7795 |
| format | Article |
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distance between any two edges is at least $r$. A $2$-matching is also called
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an induced matching. In this paper, we estimate the maximum number of
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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.</abstract><doi>10.48550/arxiv.1409.7795</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Combinatorics |
| title | On the number of $r$-matchings in a Tree |
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