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Classification and enumeration of minimum (d, 1, 3)-graphs and minimum (d, 2, 3)-graphs

โœ Scribed by Victor Klee; Howard Quaife


Publisher
Elsevier Science
Year
1977
Tongue
English
Weight
454 KB
Volume
23
Category
Article
ISSN
0095-8956

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Let \(G\) be a 3-connected \(K_{1, d}\)-free graph on \(n\) vertices. We show that \(G\) contains a 3-connected spanning subgraph of maximum degree at most \(2 d-1\). Using an earlier result of ours, we deduce that \(G\) contains a cycle of length at least \(\frac{1}{2} n^{c}\) where \(c=\left(\log