The Number of Flips Required to Obtain Non-crossing Convex Cycles

Authors:
Yoshiaki Oda;Mamoru Watanabe
Affiliations:
Department of Mathematics, Keio University, Yokohama, Japan 223-8522;Department of Computer Science and Mathematics, Kurashiki University of Science and the Arts, Kurashiki, Japan 712-8505
Venue:
Computational Geometry and Graph Theory
Year:
2008

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Abstract

In this paper, we consider Hamiltonian cycles of vertices in convex position on the plane, where, in general, these cycles contain crossing edges. We give several results concerning the minimum number of operations that delete two crossing edges, add two other edges and preserve hamiltonicity in transforming these cycles to non-crossing Hamiltonian cycles.