@article{f38a9fc8-9df5-4260-9097-ce57138daea1,
author = {Sławomir Bakalarski, Jakub  Zygadło},
title = {On the Path Sequence of a Graph},
journal = {Schedae Informaticae},
volume = {2015},
number = {Volume 24},
year = {2016},
issn = {1732-3916},
pages = {239-251},keywords = {k-path vertex cover; path sequence; list for small graphs},
abstract = {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.},
doi = {10.4467/20838476SI.16.020.4361},
url = {https://ejournals.eu/en/journal/schedae-informaticae/article/on-the-path-sequence-of-a-graph}
}