AKCE International Journal of Graphs and Combinatorics (Sep 2022)

Edge-maximal -free non-bipartite Hamiltonian graphs of odd order

  • M. M. M. Jaradat,
  • A. Baniabedalruhman,
  • M. S. Bataineh,
  • A. M. M. Jaradat,
  • A. A. Al-Rhayyel

DOI
https://doi.org/10.1080/09728600.2022.2145922
Journal volume & issue
Vol. 19, no. 3
pp. 282 – 286

Abstract

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AbstractLet [Formula: see text] denote the class of non-bipartite graphs on n vertices containing no [Formula: see text]-graph and [Formula: see text] Let [Formula: see text] denote the class of non-bipartite Hamiltonian graphs on n vertices containing no [Formula: see text]-graph and [Formula: see text] In this paper we determine [Formula: see text] by proving that for sufficiently large odd n, [Formula: see text] Furthermore, the bound is best possible. Our results confirm the conjecture made by Bataineh in 2007.

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