Geodesic
Matching complexes of small grids
Takahiro Matsushita1
1University of the Ryukyus
The electronic journal of combinatorics, Tome 26 (2019) no. 3
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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 $\Delta^m_n$, which is a generalization of the line graph of the $(n \times 2)$-grid graph. In this paper, we show that the independence complex of $\Delta^m_n$ is a wedge of spheres. This gives an answer to a problem suggested by Braun and Hough.
DOI : 10.37236/8480
Classification : 05C69, 05E45

Takahiro Matsushita  1

1 University of the Ryukyus 
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     author = {Takahiro Matsushita},
     title = {Matching complexes of small grids},
     journal = {The electronic journal of combinatorics},
     year = {2019},
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     number = {3},
     doi = {10.37236/8480},
     zbl = {1416.05214},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8480/}
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Takahiro Matsushita. Matching complexes of small grids. The electronic journal of combinatorics, Tome 26 (2019) no. 3. doi: 10.37236/8480

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