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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ligong Wang
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, Shaanxi, 710129, P.R. China
Electrical & Electronics Engineering

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On hamiltonicity of 1-tough triangle-free graphs Wei Zheng; Hajo Broersma; Ligong Wang
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.15

Abstract

Let ω(G) denote the number of components of a graph G. A connected graph G is said to be 1-tough if ω(G − X)≤|X| for all X ⊆ V(G) with ω(G − X)>1. It is well-known that every hamiltonian graph is 1-tough, but that the reverse statement is not true in general, and even not for triangle-free graphs. We present two classes of triangle-free graphs for which the reverse statement holds, i.e., for which hamiltonicity and 1-toughness are equivalent. Our two main results give partial answers to two conjectures due to Nikoghosyan.
Co-Authors Hajo Broersma Wei Zheng