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- W4307123456 abstract "We investigate the shellability of the polyhedral join $mathcal{Z}^*_M (K, L)$ of simplicial complexes $K, M$ and a subcomplex $L subset K$. We give sufficient conditions and necessary conditions on $(K, L)$ for $mathcal{Z}^*_M (K, L)$ being shellable. In particular, we show that for some pairs $(K, L)$, $mathcal{Z}^*_M (K, L)$ becomes shellable regardless of whether $M$ is shellable or not. Polyhedral joins can be applied to graph theory as the independence complex of a certain generalized version of lexicographic products of graphs which we define in this paper. The graph obtained from two graphs $G, H$ by attaching one copy of $H$ to each vertex of $G$ is a special case of this generalized lexicographic product and we give a result on the shellability of the independence complex of this graph by applying the above results." @default.
- W4307123456 created "2022-10-27" @default.
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- W4307123456 date "2022-05-08" @default.
- W4307123456 modified "2023-09-27" @default.
- W4307123456 title "Shellability of Polyhedral Joins of Simplicial Complexes and Its Application to Graph Theory" @default.
- W4307123456 doi "https://doi.org/10.48550/arxiv.2205.03869" @default.
- W4307123456 hasPublicationYear "2022" @default.
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