Geodesic
Perfect matching complexes of honeycomb graphs
Margaret Bayer1 ; Marija Jelić Milutinović2 ; Julianne Vega3
1University of Kansas
2University of Belgrade
3Maret School
The electronic journal of combinatorics, Tome 30 (2023) no. 2
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The perfect matching complex of a graph is the simplicial complex on the edge set of the graph with facets corresponding to perfect matchings of the graph. This paper studies the perfect matching complexes, $\mathcal{M}_p(H_{k \times m\times n})$, of honeycomb graphs. For $k = 1$, $\mathcal{M}_p(H_{1\times m\times n})$ is contractible unless $n\geq m=2$, in which case it is homotopy equivalent to the $(n-1)$-sphere. Also, $\mathcal{M}_p(H_{2\times 2\times 2})$ is homotopy equivalent to the wedge of two 3-spheres. The proofs use discrete Morse theory.
DOI : 10.37236/11525
Classification : 05C70, 05E45, 55P15, 57M15
Mots-clés : discrete Morse theory, topology of simplicial complexes, matching complexes

Margaret Bayer  1   ; Marija Jelić Milutinović  2   ; Julianne Vega  3

1 University of Kansas
2 University of Belgrade
3 Maret School 
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Margaret Bayer; Marija Jelić Milutinović; Julianne Vega. Perfect matching complexes of honeycomb graphs. The electronic journal of combinatorics, Tome 30 (2023) no. 2. doi: 10.37236/11525

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