The Circumference of 2-Tough Graphs
Publication Date
8-15-2026
Document Type
Article
Publication Title
Discrete Applied Mathematics
Volume
389
DOI
10.1016/j.dam.2026.03.052
First Page
280
Last Page
284
Abstract
The 2-tough conjecture, formulated in the early 70s, asserts that every 2-tough graph with 3 or more vertices is hamiltonian. This long standing conjecture was finally disproven in 2000. Here we show that for any ϵ>0, there exists a 2-tough graph G with 3 or more vertices with circumference less than (1/2+ϵ)|V(G)|.
Keywords
2-tough conjecture, 2-tough graphs, Circumference
Department
Mathematics and Statistics
Recommended Citation
Linda Lesniak and Edward Schmeichel. "The Circumference of 2-Tough Graphs" Discrete Applied Mathematics (2026): 280-284. https://doi.org/10.1016/j.dam.2026.03.052
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