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]:...
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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 |
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| Online Access: | https://doi.org/10.7151/dmgt.2020 |
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doaj-41c5d1fec32141e2b28fec9876a70c832021-09-05T17:20:23ZengSciendoDiscussiones Mathematicae Graph Theory2083-58922018-05-0138249149810.7151/dmgt.2020dmgt.2020On the Number of Disjoint 4-Cycles in Regular TournamentsMa Fuhong0Yan Jin1School of Mathematics, Shandong University, Jinan250100, P.R. ChinaSchool of Mathematics, Shandong University, Jinan250100, P.R. ChinaIn 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.https://doi.org/10.7151/dmgt.2020regular tournamentc4-freedisjoint cycles05c7005c38 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Ma Fuhong Yan Jin |
| spellingShingle |
Ma Fuhong Yan Jin On the Number of Disjoint 4-Cycles in Regular Tournaments Discussiones Mathematicae Graph Theory regular tournament c4-free disjoint cycles 05c70 05c38 |
| author_facet |
Ma Fuhong Yan Jin |
| author_sort |
Ma Fuhong |
| title |
On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_short |
On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_full |
On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_fullStr |
On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_full_unstemmed |
On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_sort |
on the number of disjoint 4-cycles in regular tournaments |
| publisher |
Sciendo |
| series |
Discussiones Mathematicae Graph Theory |
| issn |
2083-5892 |
| publishDate |
2018-05-01 |
| description |
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. |
| topic |
regular tournament c4-free disjoint cycles 05c70 05c38 |
| url |
https://doi.org/10.7151/dmgt.2020 |
| work_keys_str_mv |
AT mafuhong onthenumberofdisjoint4cyclesinregulartournaments AT yanjin onthenumberofdisjoint4cyclesinregulartournaments |
| _version_ |
1717786343251116032 |