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Complexes of graphs with bounded matching size
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
2004 (English)Report (Other academic)
Abstract [en]

For positive integers $k,n$, we investigate the simplicial complex $\nmkn$ of all graphs $G$ on vertex set $[n]$ such that every matching in $G$ has size less than $k$. This complex (along with other associated cell complexes) is found to be homotopy equivalent to a wedge of spheres. The number and dimension of the spheres in the wedge are determined, and (partially conjectural) links to other combinatorially defined complexes are described. In addition we study for positive integers $r,s$ and $k$ the simplicial complex $\bnmkrs$ of all bipartite graphs $G$ on bipartition $[r] \cup [\bar{s}]$ such that there is no matching of size $k$ in $G$, and obtain results similar to those obtained for $\nmkn$.

Place, publisher, year, edition, pages
Ithaca: ArXiv.org , 2004.
Keyword [en]
matching, homotopy type
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-23609Local ID: 3099OAI: oai:DiVA.org:liu-23609DiVA: diva2:243924
Available from: 2009-10-07 Created: 2009-10-07

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Other links

http://www.arxiv.org/abs/math.CO/0410345

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Linusson, Svante

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