Abstract
In this paper we prove the following: let G be a graph with e G 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 ⌈ re G ⧸ 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].
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