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Building Bridges pp 427–454Cite as

Recent Progress in Matching Extension

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Part of the book series: Bolyai Society Mathematical Studies ((BSMS,volume 19))

Abstract

Let G be a graph with at least 2n+2 vertices, where n is a non-negative integer. The graph G is said to be n-extendable if every matching of size n in G extends to (i.e., is a subset of) a perfect matching. The study of this concept began in earnest in the 1980’s, although it was born out of the study of canonical matching decompositions carried out in the 1970’s and before. As is often the case, in retrospect it is apparent that there are roots of this topic to be found even earlier.

In the present paper, we will begin with a brief history of the subject and then concentrate on reviewing results on n-extendability and closely related areas obtained in the last ten-fifteen years, as there already exist two surveys of the subject in 1994 and 1996, respectively.

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  1. Department of Mathematics, Vanderbilt University, Nashville, Tennessee, 37240, USA

    Michael D. Plummer

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  1. Konrad-Zuse-Zentrum für Informationstechnik Berlin (ZIB), Takustr. 7, 14195, Berlin, Germany

    Martin Grötschel

  2. Hungarian Academy of Sciences, Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, Budapest, 1053, Hungary

    Gyula O. H. Katona  & Gábor Sági  & 

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Dedicated to László Lovász on the occasion of his 60th birthday

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Plummer, M.D. (2008). Recent Progress in Matching Extension. In: Grötschel, M., Katona, G.O.H., Sági, G. (eds) Building Bridges. Bolyai Society Mathematical Studies, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85221-6_14

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