Graphs and Combinatorics

, Volume 17, Issue 2, pp 245–253 | Cite as

On the Strong Product of a k-Extendable and an l-Extendable Graph

  • Ervin Győri
  • Wilfried Imrich

Abstract.

 Let G1G2 be the strong product of a k-extendable graph G1 and an l-extendable graph G2, and X an arbitrary set of vertices of G1G2 with cardinality 2[(k+1)(l+1)/2]. We show that G1G2X contains a perfect matching. It implies that G1G2 is [(k+1)(l+1)/2]-extendable, whereas the Cartesian product of G1 and G2 is only (k+l+1)-extendable. As in the case of the Cartesian product, the proof is based on a lemma on the product of a k-extendable graph G and K2. We prove that GK2 is (k+1)-extendable, and, a bit surprisingly, it even remains (k+1)-extendable if we add edges to it.

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Copyright information

© Springer-Verlag Tokyo 2001

Authors and Affiliations

  • Ervin Győri
    • 1
  • Wilfried Imrich
    • 2
  1. 1. Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, H-1053 Budapest, Hungary. e-mail: ervin@renyi.huHU
  2. 2. Montanuniversität Leoben, A-8700 Leoben, Austria. e-mail: imrich@unileoben.ac.atAT

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