Jump number of dags having Dilworth number 2

Chein, Michel; Habib, Michel

doi:10.1016/0166-218x(84)90002-7

Cited by 12 publications

(1 citation statement)

References 4 publications

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“…Up to our knowledge, its computational classification is still open for lattices. Nevertheless, polynomial time algorithms are known for several classes of ordered sets (see [4,5,6,7,24,25,11]).…”

Section: Introductionmentioning

confidence: 99%

Crossing-Free Acyclic Hamiltonian Path Completion for Planar st-Digraphs

Mchedlidze

Symvonis

2009

Algorithms and Computation

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Abstract. In this paper we study the problem of existence of a crossing-free acyclic hamiltonian path completion (for short, HP-completion) set for embedded upward planar digraphs. In the context of book embeddings, this question becomes: given an embedded upward planar digraph G, determine whether there exists an upward 2-page book embedding of G preserving the given planar embedding. Given an embedded st-digraph G which has a crossing-free HP-completion set, we show that there always exists a crossing-free HP-completion set with at most two edges per face of G. For an embedded N -free upward planar digraph G, we show that there always exists a crossing-free acyclic HP-completion set for G which, moreover, can be computed in linear time. For a width-k embedded planar st-digraph G, we show that we can be efficiently test whether G admits a crossing-free acyclic HP-completion set.

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