On the Number of Disjoint 4-Cycles in Regular Tournaments
In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r − 1 contains at least 2116r-103${{21} \over {16}}r - {{10} \over 3}$ disjoint directed 4-cycles. Our result is an improvement of Lichiardopol’s theorem when taking q = 4 [Discrete Math. 310 (2010) 2567–2570]:...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2018-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2020 |
| Summary: | In this paper, we prove that for an integer r ≥ 1, every regular tournament T of degree 3r − 1 contains at least 2116r-103${{21} \over {16}}r - {{10} \over 3}$ disjoint directed 4-cycles. Our result is an improvement of Lichiardopol’s theorem when taking q = 4 [Discrete Math. 310 (2010) 2567–2570]: for given integers q ≥ 3 and r ≥ 1, a tournament T with minimum out-degree and in-degree both at least (q − 1)r − 1 contains at least r disjoint directed cycles of length q. |
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| ISSN: | 2083-5892 |