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Finite Separating Sets in Locally Finite Graphs

✍ Scribed by H.A. Jung; M.E. Watkins

Publisher: Elsevier Science
Year: 1993
Tongue: English
Weight: 386 KB
Volume: 59
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1993.1050

No coin nor oath required. For personal study only.

✦ Synopsis

An ((m, n))-separator of an infinite graph (\Gamma) is a smallest finite set of vertices whose deletion leaves at least (m) finite components and at least (n) infinite components. It is shown that a vertex of (\Gamma) of finite valence belongs to only finitely many ((0,2))-separators. Various results concerning the interrelation of ((m, n))-separators (especially ((0,2))-separators) are obtained for locally finite graphs. Particular attention is given in the case that (\Gamma) is vertex-transitive or edge-transitive. Co 1993 Academic Press. Inc.

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