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- W4287668568 abstract "A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. The paper is concerned with the linkedness of the graphs of cubical polytopes. A graph with at least $2k$ vertices is textit{$k$-linked} if, for every set of $k$ disjoint pairs of vertices, there are $k$ vertex-disjoint paths joining the vertices in the pairs. We say that a polytope is textit{$k$-linked} if its graph is $k$-linked. In a previous paper cite{BuiPinUgo20a} we proved that every cubical $d$-polytope is $floor{d/2}$-linked. Here we strengthen this result by establishing the $floor{(d+1)/2}$-linkedness of cubical $d$-polytopes, for every $dne 3$. A graph $G$ is {it strongly $k$-linked} if it has at least $2k+1$ vertices and, for every vertex $v$ of $G$, the subgraph $G-v$ is $k$-linked. We say that a polytope is (strongly) textit{$k$-linked} if its graph is (strongly) $k$-linked. In this paper, we also prove that every cubical $d$-polytope is strongly $floor{d/2}$-linked, for every $dne 3$. These results are best possible for this class of polytopes." @default.
- W4287668568 created "2022-07-25" @default.
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- W4287668568 date "2020-09-12" @default.
- W4287668568 modified "2023-10-14" @default.
- W4287668568 title "The linkedness of cubical polytopes: beyond the cube" @default.
- W4287668568 doi "https://doi.org/10.48550/arxiv.2009.07071" @default.
- W4287668568 hasPublicationYear "2020" @default.
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