Longest cycles in 3-connected graphs (Q1363662)
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scientific article; zbMATH DE number 1047054
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Longest cycles in 3-connected graphs |
scientific article; zbMATH DE number 1047054 |
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Longest cycles in 3-connected graphs (English)
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10 August 1997
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The author shows that in a non-Hamiltonian 3-connected graph there exist a cycle \(C\) and three independent vertices \(u_1\), \(u_2\), \(u_3\) such that \(| C|\geq d(u_1)+ d(u_2)+ d(u_3)- | N(u_1)\cap N(u_2)\cap N(u_3)|\), where \(d(u_i)= | N(u_i)|\) is the degree of \(u_i\) \((i= 1,2,3)\). Some corollaries are supplied.
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cycle
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