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21st Cumberland Conference on Graph Theory, Combinatorics, and Computing ---In Honor of Mike Plummer's 70th Birthday
May 15-17, 2008
Vanderbilt University
Nashville, TN, USA

Organizers
Mark Ellingham and Gexin Yu

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Graphs in which every minimal set of edges covering edges is minimum
by
Bert Hartnell
Saint Mary's University
Coauthors: Allan Frendrup and Preben Vestergaard

There are four related natural covering problems: vertices covering vertices (or edges) and edges covering vertices (or edges). Three of these have been studied in the context of what are the graphs such that every minimal set with the required property is minimum. Here we examine the 4th case, graphs in which every minimal set of edges covering edges is minimum. Such graphs are a subclass of the equimatchable graphs (Lesk, Plummer and Pulleyblank). For graphs of girth at least 5, a simple characterization is obtained.

Date received: March 5, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cawn-11.