Bounding the Size of Equimatchable Graphs of Fixed Genus
نویسندگان
چکیده
A graph G is said to be equimatchable if every matching in G extends to (i.e., is a subset of) a maximum matching in G. In a 2003 paper, Kawarabayashi, Plummer and Saito showed that there are only a finite number of 3-connected equimatchable planar graphs. In the present paper, this result is extended by showing that in a surface of any fixed genus (orientable or non-orientable), there are only a finite number of 3-connected equimatchable graphs having a minimal embedding of representativity at least three. The proof makes use of the Gallai-Edmonds decomposition theorem for matchings.
منابع مشابه
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ورودعنوان ژورنال:
- Graphs and Combinatorics
دوره 25 شماره
صفحات -
تاریخ انتشار 2009