On arithmetic progressions of cycle lengths in graphs (Q2703026)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On arithmetic progressions of cycle lengths in graphs |
scientific article |
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21 January 2002
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cycle length
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girth
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On arithmetic progressions of cycle lengths in graphs (English)
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The author settles a question of Haggkvist and Scott by proving that, for \(k \geq 2\), a bipartite graph of girth \(g\) and average degree at least \(4k\) contains cycles of \((g/2 - 1)k\) consecutive even lengths. He also gives a short proof of Bondy and Simonovits' theorem that a graph of order \(n\) and size at least \(8(k-1)n^{1+1/k}\) has a \(2k\)-cycle.
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