Hamilton paths in toroidal graphs

Authors:
Robin Thomas;Xingxing Yu;Wenan Zang
Affiliations:
School of Mathematics, Georgia Institute of Technology, Atlanta, GA;School of Mathematics, Georgia Institute of Technology, Atlanta, GA and Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China;Department of Mathematics, University of Hong Kong, Hong Kong, China
Venue:
Journal of Combinatorial Theory Series B
Year:
2005

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Abstract

Tutte has shown that every 4-connected planar graph contains a Hamilton cycle. Grünbaum and Nash-Williams independently conjectured that the same is true for toroidal graphs. In this paper, we prove that every 4-connected toroidal graph contains a Hamilton path.