Circumference and girth
Cun‐Quan Zhang · Journal of Graph Theory · 1989
Abstract Let G be 2‐connected graph with girth g and minimum degree d. Then each pair of vertices of G is joined by a path of length at least max{1/2(d − 1)g, (d − 3/2)(g − 4) + 2} if g ⩾ 4, and the length of a longest cycle of G is at least max{[(d − 1)(g − 2) + 2], [(2d − 3)(g − 4) + 4]}.