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Horizons in Combinatorics/16th Shanks Lecture Series
May 21-24, 2001
Vanderbilt University
Nashville, TN, USA

Organizers
Paul Edelman, Mark Ellingham, Jonathan Farley, Mike Plummer, Jerry Spinrad

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Chords of longest circuits of graphs embedded in torus or Klein bottle
by
Xuechao Li
West Virginia University
Coauthors: C.Q.Zhang, West Virginia University

Chords of Longest Circuits of Graphs Embedded in Torus and Klein Bottle

Chords of Longest Circuits of Graphs Embedded in Torus and Klein Bottle

Xuechao Li and Cun-Quan Zhang 1
Department of Mathematics, P.O.Box 6310
West Virginia University
Morgantown, West Virginia. 26506
email: xuec@math.wvu.edu, cqzhang@math.wvu.edu

Abstract

Thomassen conjectured that every longest circuit of a 3-connected graph has a chord. It is proved in this paper that every longest circuit of a 4-connected graph embedded in a torus or Klein bottle has a chord.

Footnotes:

1Partially supported by the National Security Agency under Grant MDA904-00-1-00614

Date received: February 19, 2001

Copyright © 2001 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 Mathematical Conference Abstracts. Document # cags-04.