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On Chvátal’s Conjecture for the Hamiltonicity of 1-Tough Graphs and Their Complements

Authors: Shin-Shin Kao, Hsun Su, Yuan-Kang Shih


In this paper, we show that the conjecture of Chv tal, which states that any 1-tough graph is either a Hamiltonian graph or its complement contains a specific graph denoted by F, does not hold in general. More precisely, it is true only for graphs with six or seven vertices, and is false for graphs with eight or more vertices. A theorem is derived as a correction for the conjecture.

Keywords: Hamiltonian, complement, degree sum, tough

Digital Object Identifier (DOI):

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