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 (AKCE International Journal of Graphs and Combinatorics, 2022)
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.