On Petersen's graph theorem

Nathan Linial*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In 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{plus 45 degree rule}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].

Original languageAmerican English
Pages (from-to)53-56
Number of pages4
JournalDiscrete Mathematics
Issue number1
StatePublished - 1981
Externally publishedYes


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