On Petersen's graph theorem

AbstractIn this paper we prove the following: let G be a graph with eG edges, which is (k − 1)-edge- connected, and with all valences ⩾k. Let 1⩽r⩽k be an integer, then G contains a spanning subgraph H, so that all valences in H are ⩾r, with no more than ⌈reG⧸k⌉ edges. The proof is based on a useful extension of Tutte's factor theorem [4,5], due to Lovász [3]. For other extensions of Petersen's theorem, see [6,7,8]