413 research outputs found

    Minimum Degree and Disjoint Cycles in Generalized Claw-Free Graphs

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    https://digitalcommons.memphis.edu/speccoll-faudreerj/1217/thumbnail.jp

    On some intriguing problems in Hamiltonian graph theory -- A survey

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    We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, tt-tough graphs, and claw-free graphs

    Regularity of Edge Ideals and Their Powers

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    We survey recent studies on the Castelnuovo-Mumford regularity of edge ideals of graphs and their powers. Our focus is on bounds and exact values of  reg I(G)\text{ reg } I(G) and the asymptotic linear function  reg I(G)q\text{ reg } I(G)^q, for q≥1,q \geq 1, in terms of combinatorial data of the given graph G.G.Comment: 31 pages, 15 figure

    Matchings, coverings, and Castelnuovo-Mumford regularity

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    We show that the co-chordal cover number of a graph G gives an upper bound for the Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial upper bounds of regularity for edge ideals are then easy consequences of covering results from graph theory, and we derive new upper bounds by looking at additional covering results.Comment: 12 pages; v4 has minor changes for publicatio

    A look at cycles containing specified elements of a graph

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    AbstractThis article is intended as a brief survey of problems and results dealing with cycles containing specified elements of a graph. It is hoped that this will help researchers in the area to identify problems and areas of concentration
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