Bipartite permutation graphs

Spinrad, Jeremy P.; Brandstädt, Andreas; Stewart, Lorna

doi:10.1016/s0166-218x(87)80003-3

Cited by 225 publications

(132 citation statements)

References 19 publications

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“…We will use the following characterization of bipartite permutation graphs given by Spinrad, Brandstädt, and Stewart [18] (see also [3]). Let G be a bipartite graph and let V 1 , V 2 be a bipartition of V (G).…”

Section: Clique-matchingmentioning

confidence: 99%

Hadwiger Number of Graphs with Small Chordality

Golovach

Heggernes

Hof

et al. 2014

Graph-Theoretic Concepts in Computer Science

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The Hadwiger number of a graph G is the largest integer h such that G has the complete graph K h as a minor. We show that the problem of determining the Hadwiger number of a graph is NP-hard on co-bipartite graphs, but can be solved in polynomial time on cographs and on bipartite permutation graphs. We also consider a natural generalization of this problem that asks for the largest integer h such that G has a minor with h vertices and diameter at most s. We show that this problem can be solved in polynomial time on AT-free graphs when s ≥ 2, but is NP-hard on chordal graphs for every fixed s ≥ 2.

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Section: Clique-matchingmentioning

confidence: 99%

Hadwiger Number of Graphs with Small Chordality

Golovach

Heggernes

Hof

et al. 2014

Graph-Theoretic Concepts in Computer Science

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“…contains an s-star, 0 otherwise, and Concerning the running time, first, a strong ordering of the vertices can be computed in linear time [28]. Second, the table in the dynamic program has O(k 2 ) entries and initialization as well as updating works in O(s 2 ) time.…”

Section: Bipartite Permutation Graphsmentioning

confidence: 99%

Partitioning Perfect Graphs into Stars

Bevern

Bredereck

Bulteau

et al. 2016

Journal of Graph Theory

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The partition of graphs into "nice" subgraphs is a central algorithmic problem with strong ties to matching theory. We study the partitioning of undirected graphs into same-size stars, a problem known to be NPcomplete even for the case of stars on three vertices. We perform a thorough computational complexity study of the problem on subclasses of perfect graphs and identify several polynomial-time solvable cases, for example, on interval graphs and bipartite permutation graphs, and also NP-complete cases, for example, on grid graphs and chordal graphs.

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“…The subclass of permutation graphs consisting of those that are bipartite has also been studied, with structure studied initially in [27,28], optimization problems in [1,4,12,13], and enumeration in [24]. We study a different class of bipartite graphs that properly contains the bipartite permutation graphs.…”

Section: Theorem 11 [8 9 11] For a Graph G The Following Conditimentioning

confidence: 99%

Permutation bigraphs and interval containments

Saha

Basu²,

Sen

et al. 2014

Discrete Applied Mathematics

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A bipartite graph with partite sets X and Y is a permutation bigraph if there are two linear orderings of its vertices so that xy is an edge for x ∈ X and y ∈ Y if and only if x appears later than y in the first ordering and earlier than y in the second ordering. We characterize permutation bigraphs in terms of representations using intervals. We determine which permutation bigraphs are interval bigraphs or indifference bigraphs in terms of the defining linear orderings. Finally, we show that interval containment posets are precisely those whose comparability bigraphs are permutation bigraphs, via a theorem showing that a directed version of interval containment provides no more generality than ordinary interval containment representation of posets.

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Bipartite permutation graphs

Cited by 225 publications

References 19 publications

Hadwiger Number of Graphs with Small Chordality

Hadwiger Number of Graphs with Small Chordality

Partitioning Perfect Graphs into Stars

Permutation bigraphs and interval containments

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