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 -