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The clique operator on matching and chessboard graphs |
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| Authors: | F Larrión R Villarroel-Flores |
| Institution: | a Instituto de Matemáticas, Universidad Nacional Autónoma de México, México 04510 D.F., Mexico b Universidad Autónoma Metropolitana, Depto. de Ingeniería Eléctrica., Av. San Rafael Atlixco 186. Col Vicentina. Del. Iztapalapa., México 09340 D.F., Mexico c Centro de Investigación en Matemáticas, Universidad Autónoma del Estado de Hidalgo, Carr. Pachuca-Tulancingo km. 4.5, Pachuca 42184 Hgo., Mexico |
| Abstract: | Given positive integers m,n, we consider the graphs Gn and Gm,n whose simplicial complexes of complete subgraphs are the well-known matching complex Mn and chessboard complex Mm,n. Those are the matching and chessboard graphs. We determine which matching and chessboard graphs are clique-Helly. If the parameters are small enough, we show that these graphs (even if not clique-Helly) are homotopy equivalent to their clique graphs. We determine the clique behavior of the chessboard graph Gm,n in terms of m and n, and show that Gm,n is clique-divergent if and only if it is not clique-Helly. We give partial results for the clique behavior of the matching graph Gn. |
| Keywords: | Clique graph Clique divergence Matching complex Chessboard complex Homotopy type |
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