Matching complexes of small grids

2018/12/28 by Takahiro Matsushita, Matsushita, Takahiro · 1 citation
Computer Science · Mathematics · #Topological and Geometric Data Analysis #Advanced Combinatorial Mathematics #Digital Image Processing Techniques

paper · pdf · doi:10.48550/arxiv.1812.11000

Abstract

The matching complex M(G) of a simple graph G is the simplicial complex consisting of the matchings on G. The matching complex M(G) is isomorphic to the independence complex of the line graph L(G). Braun and Hough introduced a family of graphs Δ^m_n, which is a generalization of the line graph of the (n × 2)-grid graph. In this paper, we show that the independence complex of Δ^m_n is a wedge of spheres. This gives an answer to a problem suggested by Braun and Hough.

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• Independence Complexes of Hexagonal Grid Graphs

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