413 research outputs found
Minimum Degree and Disjoint Cycles in Generalized Claw-Free Graphs
https://digitalcommons.memphis.edu/speccoll-faudreerj/1217/thumbnail.jp
On some intriguing problems in Hamiltonian graph theory -- A survey
We survey results and open problems in Hamiltonian graph theory centred around three themes: regular graphs, -tough graphs, and claw-free graphs
Regularity of Edge Ideals and Their Powers
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 and the asymptotic linear function , for in terms of combinatorial data of the given graph Comment: 31 pages, 15 figure
Matchings, coverings, and Castelnuovo-Mumford regularity
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
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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