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arXiv · 2406.17089

Spectral conditions of pancyclicity for t-tough graphs

Vladimir I. Benediktovich
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Abstract

More than 40 years ago Chv\'atal introduced a new graph invariant, which he called graph toughness. From then on a lot of research has been conducted, mainly related to the relationship between toughness conditions and the existence of cyclic structures, in particular, determining whether the graph is Hamiltonian and pancyclic. A pancyclic graph is certainly Hamiltonian, but not conversely. Bondy in 1976, however, suggested the "metaconjecture" that almost any nontrivial condition on a graph which implies that the graph is Hamiltonian also implies that the graph is pancyclic. We confirm the Bondy conjecture for t-tough graphs in the case when $t\in \{ 1;2;3\}$ in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph.

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Vladimir I. Benediktovich. 2024-06-24. Spectral conditions of pancyclicity for t-tough graphs. https://arxiv.org/abs/2406.17089

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