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Matching Complexes, Bounded Degree Graph Complexes, and Weight Spaces of GLn-Complexes

โœ Scribed by Dikran B. Karaguezian; Victor Reiner; Michelle L. Wachs

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
124 KB
Volume
239
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

We present a technique for lifting results on the homology of matching complexes of certain types of graphs and hypergraphs to general bounded degree graph complexes. This technique is based on our observation that homological results of Bouc on matching complexes, of Reiner and Roberts on bounded degree graph complexes, and of Jozefiak and Weyman on Koszul complexes are all equivalent.

แฎŠ 2001 Academic Press

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## Abstract The Matchingโ€Cut problem is the problem to decide whether a graph has an edge cut that is also a matching. Previously this problem was studied under the name of the Decomposable Graph Recognition problem, and proved to be ${\cal{NP}}$โ€complete when restricted to graphs with maximum deg