24,522 research outputs found

    Hitting minors, subdivisions, and immersions in tournaments

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    The Erd\H{o}s-P\'osa property relates parameters of covering and packing of combinatorial structures and has been mostly studied in the setting of undirected graphs. In this note, we use results of Chudnovsky, Fradkin, Kim, and Seymour to show that, for every directed graph HH (resp. strongly-connected directed graph HH), the class of directed graphs that contain HH as a strong minor (resp. butterfly minor, topological minor) has the vertex-Erd\H{o}s-P\'osa property in the class of tournaments. We also prove that if HH is a strongly-connected directed graph, the class of directed graphs containing HH as an immersion has the edge-Erd\H{o}s-P\'osa property in the class of tournaments.Comment: Accepted to Discrete Mathematics & Theoretical Computer Science. Difference with the previous version: use of the DMTCS article class. For a version with hyperlinks see the previous versio

    A note on circular chromatic number of graphs with large girth and similar problems

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    In this short note, we extend the result of Galluccio, Goddyn, and Hell, which states that graphs of large girth excluding a minor are nearly bipartite. We also prove a similar result for the oriented chromatic number, from which follows in particular that graphs of large girth excluding a minor have oriented chromatic number at most 55, and for the ppth chromatic number χp\chi_p, from which follows in particular that graphs GG of large girth excluding a minor have χp(G)≤p+2\chi_p(G)\leq p+2

    Spartan Daily, March 7, 2006

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    Volume 126, Issue 23https://scholarworks.sjsu.edu/spartandaily/10223/thumbnail.jp
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