Matching and independence complexes related to small grids

Benjamin Braun, Wesley K. Hough

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The topology of the matching complex for the 2×n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(Δm n) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(Δm n). Furthermore, we determine the Euler characteristic of Ind(Δm n) and prove that several homology groups of Ind(Δm n) are non-zero.

Original languageEnglish
Article number#P4.18
JournalElectronic Journal of Combinatorics
Issue number4
StatePublished - Oct 20 2017

Bibliographical note

Publisher Copyright:
© 2017, Australian National University. All rights reserved.


  • Grid graphs
  • Homology
  • Independence complexes
  • Recursions

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics
  • Applied Mathematics


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