On Petersen's graph theorem

Nathan Linial

doi:10.1016/0012-365X(81)90257-0

On Petersen's graph theorem

Nathan Linial^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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{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 language	American English
Pages (from-to)	53-56
Number of pages	4
Journal	Discrete Mathematics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1016/0012-365X(81)90257-0
State	Published - 1981
Externally published	Yes

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title = "On Petersen's graph theorem",

abstract = "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 Lov{\'a}sz [3]. For other extensions of Petersen's theorem, see [6,7,8].",

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AB - 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].

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On Petersen's graph theorem

Abstract

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