The least number of 3-cycles (cycles of length 3) that a hamiltonian tournament of order n can contain is n -2 (see [3]). Since each complete strongly connected digraph contains a spanning hamiltonian subtournament (see [2]), n-2 is also the least number of 3-cycles for these digraphs. In this pape
On the number of cycles possible in digraphs with large girth
β Scribed by Eric W. Allender
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 682 KB
- Volume
- 10
- Category
- Article
- ISSN
- 0166-218X
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It was proved by Hell and Zhu that, if G is a series-parallel graph of girth at least 2 (3k -1)/2 , then Ο c (G) β€ 4k/(2k -1). In this article, we prove that the girth requirement is sharp, i.e., for any k β₯ 2, there is a series-parallel graph G of girth 2 (3k -1)/2 -1 such that Ο c (G) > 4k/(2k -1)
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