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- W2949202367 abstract "We call a digraph {em $h$-semicomplete} if each vertex of the digraph has at most $h$ non-neighbors, where a non-neighbor of a vertex $v$ is a vertex $u neq v$ such that there is no edge between $u$ and $v$ in either direction. This notion generalizes that of semicomplete digraphs which are $0$-semicomplete and tournaments which are semicomplete and have no anti-parallel pairs of edges. Our results in this paper are as follows. (1) We give an algorithm which, given an $h$-semicomplete digraph $G$ on $n$ vertices and a positive integer $k$, in $(h + 2k + 1)^{2k} n^{O(1)}$ time either constructs a path-decomposition of $G$ of width at most $k$ or concludes correctly that the pathwidth of $G$ is larger than $k$. (2) We show that there is a function $f(k, h)$ such that every $h$-semicomplete digraph of pathwidth at least $f(k, h)$ has a semicomplete subgraph of pathwidth at least $k$. One consequence of these results is that the problem of deciding if a fixed digraph $H$ is topologically contained in a given $h$-semicomplete digraph $G$ admits a polynomial-time algorithm for fixed $h$." @default.
- W2949202367 created "2019-06-27" @default.
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- W2949202367 date "2015-07-07" @default.
- W2949202367 modified "2023-10-16" @default.
- W2949202367 title "On the pathwidth of almost semicomplete digraphs" @default.
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- W2949202367 doi "https://doi.org/10.48550/arxiv.1507.01934" @default.
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