59 research outputs found

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    LIPIcs, Volume 274, ESA 2023, Complete Volume

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    LIPIcs, Volume 274, ESA 2023, Complete Volum

    LIPIcs, Volume 258, SoCG 2023, Complete Volume

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    LIPIcs, Volume 258, SoCG 2023, Complete Volum

    Directed Acyclic Outerplanar Graphs Have Constant Stack Number

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    The stack number of a directed acyclic graph GG is the minimum kk for which there is a topological ordering of GG and a kk-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We prove that the stack number of directed acyclic outerplanar graphs is bounded by a constant, which gives a positive answer to a conjecture by Heath, Pemmaraju and Trenk [SIAM J. Computing, 1999]. As an immediate consequence, this shows that all upward outerplanar graphs have constant stack number, answering a question by Bhore et al. [GD 2021] and thereby making significant progress towards the problem for general upward planar graphs originating from Nowakowski and Parker [Order, 1989]. As our main tool we develop the novel technique of directed HH-partitions, which might be of independent interest. We complement the bounded stack number for directed acyclic outerplanar graphs by constructing a family of directed acyclic 2-trees that have unbounded stack number, thereby refuting a conjecture by N\"ollenburg and Pupyrev [arXiv:2107.13658, 2021]

    LIPIcs, Volume 244, ESA 2022, Complete Volume

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    LIPIcs, Volume 244, ESA 2022, Complete Volum

    LIPIcs, Volume 248, ISAAC 2022, Complete Volume

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    LIPIcs, Volume 248, ISAAC 2022, Complete Volum

    A Sublinear Bound on the Page Number of Upward Planar Graphs

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    The page number of a directed acyclic graph G is the minimum k for which there is a topological ordering of G and a k-coloring of the edges such that no two edges of the same color cross, i.e., have alternating endpoints along the topological ordering. We address the long-standing open problem asking for the largest page number among all upward planar graphs. We improve the best known lower bound to 5 and present the first asymptotic improvement over the trivial O(n) upper bound, where n denotes the number of vertices in G. Specifically, we first prove that the page number of every upward planar graph is bounded in terms of its width, as well as its height. We then combine both approaches to show that every n-vertex upward planar graph has page number O(n2/3log(n)2/3)O(n^{2/3} \log(n)^{2/3})

    Programming Languages and Systems

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    This open access book constitutes the proceedings of the 29th European Symposium on Programming, ESOP 2020, which was planned to take place in Dublin, Ireland, in April 2020, as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The actual ETAPS 2020 meeting was postponed due to the Corona pandemic. The papers deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems

    Planarity Variants for Directed Graphs

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