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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University of Zielona Góra
2018-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2020 |
| _version_ | 1797718009445351424 |
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| author | Ma Fuhong Yan Jin |
| author_facet | Ma Fuhong Yan Jin |
| author_sort | Ma Fuhong |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-12T08:44:44Z |
| format | Article |
| id | doaj.art-41c5d1fec32141e2b28fec9876a70c83 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T08:44:44Z |
| publishDate | 2018-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-41c5d1fec32141e2b28fec9876a70c832023-09-02T16:29:57ZengUniversity of Zielona GóraDiscussiones 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 |
| 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 |
| title | 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_short | On the Number of Disjoint 4-Cycles in Regular Tournaments |
| title_sort | on the number of disjoint 4 cycles in regular tournaments |
| 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 |