Volume 51, Number 3, July-September 2017
|Page(s)||857 - 873|
|Published online||28 September 2017|
On matching extendability of lexicographic products∗
1 FAMNIT and Andrej Marušič Institute, University of Primorska, 6000 Koper, Slovenia.
2 Bogazici University, Dept. of Industrial Engineering, 34342, Bebek, Istanbul, Turkey.
3 Gebze Technical University, Computer Engineering Dept., 41400 Gebze, Kocaeli, Turkey .
4 Andrej Marušič Institute, University of Primorska, Koper, Slovenia, and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia.
Received: 6 March 2016
Accepted: 27 October 2016
A graph G of even order is ℓ-extendable if it is of order at least 2ℓ + 2, contains a matching of size ℓ, and if every such matching is contained in a perfect matching of G. In this paper, we study the extendability of lexicographic products of graphs. We characterize graphs G and H such that their lexicographic product is not 1-extendable. We also provide several conditions on the graphs G and H under which their lexicographic product is 2-extendable.
Mathematics Subject Classification: 05C70 / 05C76
Key words: ℓ-extendable graphs / lexicographic product / Tutte’s Theorem
© EDP Sciences, ROADEF, SMAI 2017
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