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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.

Keywords

Perfect Match Strong Product 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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