A Dirac theorem for trestles

Abstract

A k-subtrestle in a graph G is a 2-connected subgraph of G of maximum degree at most k. We prove a lower bound on the order of a largest k-subtrestle of G in terms of k and the minimum degree of G. A corollary of our result is that every 2-connected graph with n vertices and minimum degree at least 2n/(k+2) contains a spanning k-subtrestle. This corollary is an extension of Dirac’s theorem.