Convex programming and circumference of 3-connected graphs of low genus
The circumference of a graph \(G\) is the length of a longest cycle in \(G\). We show that, if \(G\) is a 3-connected graph embeddable in the plane, the projective plane, the torus, or the Klein bottle, then \(G\) has circumference at least \((1/6)\times|V(G)|^{0.4}+1\). This improves a result of \textit{B. Jackson} and \textit{N. C. Wormald} [J. Comb. Theory, Ser. B 54, No. 2, 291-321 (1992; Zbl 0696.05031)].
scientific article; zbMATH DE number 1006484