13 research outputs found

    Oriented trees and paths in digraphs

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    Which conditions ensure that a digraph contains all oriented paths of some given length, or even a all oriented trees of some given size, as a subgraph? One possible condition could be that the host digraph is a tournament of a certain order. In arbitrary digraphs and oriented graphs, conditions on the chromatic number, on the edge density, on the minimum outdegree and on the minimum semidegree have been proposed. In this survey, we review the known results, and highlight some open questions in the area

    Dominators in Directed Graphs: A Survey of Recent Results, Applications, and Open Problems

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    The computation of dominators is a central tool in program optimization and code generation, and it has applications in other diverse areas includingconstraint programming, circuit testing, and biology. In this paper we survey recent results, applications, and open problems related to the notion of dominators in directed graphs,including dominator verification and certification, computing independent spanning trees, and connectivity and path-determination problems in directed graphs

    Mader's conjecture is true for path-star trees

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    W. Mader [J graph Theory 65 (2010),61-69] conjectured that for any tree TT of order tt, every kk-connected graph GG with minimum degree at least ⌊3k2⌋+t−1\lfloor\frac{3k}{2}\rfloor+t-1 contains a subtree T′≅TT'\cong T such that G−V(T′)G-V(T') is kk-connected. The conjecture is true when TT is a path; k=1k=1; partially k=2k=2. In this paper, we show that Mader's conjecture is true when TT is a path-star.Comment: 8 page

    Connectivity keeping spiders in k-connected graphs

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    W. Mader [J. Graph Theory 65 (2010), 61--69] conjectured that for any tree TT of order mm, every kk-connected graph GG with δ(G)≥⌊3k2⌋+m−1\delta(G)\geq\lfloor\frac{3k}{2}\rfloor+m-1 contains a tree T′≅TT'\cong T such that G−V(T′)G-V(T') remains kk-connected. In this paper, we confirm Mader's conjecture for all the spider-trees.Comment: 9 page

    Subject Index Volumes 1–200

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    Proceedings of the 10th Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications

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    Introduction to Graph Theory

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    Higher Education Mathematic

    27th Annual European Symposium on Algorithms: ESA 2019, September 9-11, 2019, Munich/Garching, Germany

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