Complexes of graphs with bounded matching size
2008 (English)In: Journal of Algebraic Combinatorics, ISSN 0925-9899, E-ISSN 1572-9192, Vol. 27, no 3, 331-349 p.Article in journal (Refereed) Published
For positive integers k, n, we investigate the simplicial complex NMk(n) 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 BNMk(r, s) of all bipartite graphs G on bipartition [r] boolean OR [(s) over bar] such that there is no matching of size k in G, and obtain results similar to those obtained for NMk(n).
Place, publisher, year, edition, pages
2008. Vol. 27, no 3, 331-349 p.
critical, trees of triangles, Gallai-Edmonds, morse-theory, topology
IdentifiersURN: urn:nbn:se:kth:diva-17447DOI: 10.1007/s10801-007-0092-1ISI: 000254849100006ScopusID: 2-s2.0-42149171166OAI: oai:DiVA.org:kth-17447DiVA: diva2:335491
QC 201005252010-08-052010-08-05Bibliographically approved