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On the Path Sequence of a Graph

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Bakalarski S., Zygadło J.

Schedae Informaticae

2015

vol. 24

A subset S of vertices of a graph G = (V,E) is called a k-path vertex cover if every path on k vertices in G contains at least one vertex from S. Denote by Ψk (G) the minimum cardinality of a k-path vertex cover in G and form a sequence Ψ (G) = (Ψ1 (G), Ψ2 (G), . . . , Ψ|V| (G)), called the path sequence of G. In this paper we prove necessary and sufficient conditions for two integers to appear on fixed positions in Ψ(G). A complete list of all possible path sequences (with multiplicities) for small connected graphs is also given.

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1 Schedae Informaticae

1 2015

1 Bakalarski S.

1 Zygadło J.

Search results

On the Path Sequence of a Graph