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Graphs Avoiding k-matchings

Part of the Lecture Notes in Mathematics book series (LNM, volume 1928)

We review the main known results about the complex NM n , k of graphs on n vertices that do not contain a k-matching;these results are due to Linusson, Shareshian, and Welker [95 ].Their most prominent achievement is the result that NM n , k is homotopy equivalent to a wedge of spheres of dimension 3k–4; the number of spheres in the wedge is a polynomial in n for each k.They proved a similar formula for the complex NM m + n , k (K m , n )of subgraphs of K m , n that do not contain a k-matching.

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© Springer-Verlag Berlin Heidelberg 2008

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