Hamilton cycles in regular 3-connected graphs (Q1208363)

Let \(G\) be a 3-connected \(k\)-regular graph on \(n\) vertices. It is known that \(G\) is Hamiltonian if \(k\geq 14\) and \(n\leq 3k+4\), and it has been conjectured that even \(k\geq 4\) and \(n\geq 4k\) imply Hamiltonicity. In the present paper it is shown that \(G\) is Hamiltonian if \(k\geq 63\) and \(n\leq{22\over 7}k\).