TY - JOUR

T1 - On Petersen's graph theorem

AU - Linial, Nathan

PY - 1981

Y1 - 1981

N2 - 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].

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].

UR - http://www.scopus.com/inward/record.url?scp=49149139663&partnerID=8YFLogxK

U2 - 10.1016/0012-365X(81)90257-0

DO - 10.1016/0012-365X(81)90257-0

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AN - SCOPUS:49149139663

SN - 0012-365X

VL - 33

SP - 53

EP - 56

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1

ER -