Another cycle structure theorem for Hamiltonian graphs (Q1297455)
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scientific article; zbMATH DE number 1321809
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Another cycle structure theorem for Hamiltonian graphs |
scientific article; zbMATH DE number 1321809 |
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Another cycle structure theorem for Hamiltonian graphs (English)
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25 October 1999
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This paper shows that for a Hamiltonian graph \(G\) of order \(n\), if non-adjacent vertices \(x\) and \(y\) of distance 2 on a Hamiltonian cycle satisfy \(d(x)+d(y)\geq n\), then \(G\) is either pancyclic or bipartite except only for the \(n-1\)-cycle and the 3-cycle \((d(x)\) is the degree of \(x\) and \(d(y)\) of \(y\)).
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Hamiltonian graph
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pancyclic graph
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cycle
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