On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m
Gutin and Rafiey [Multipartite tournaments with small number of cycles, Australas J. Combin. 34 (2006) 17–21] raised the following two problems: (1) Let m ∈ {3, 4, . . ., n}. Find a characterization of strong n-partite tournaments having exactly n − m + 1 cycles of length m; (2) Let 3 ≤ m ≤ n and n...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2021-02-01
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| Series: | Discussiones Mathematicae Graph Theory |
| Subjects: | |
| Online Access: | https://doi.org/10.7151/dmgt.2167 |
| _version_ | 1797713243552088064 |
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| author | Guo Qiaoping Meng Wei |
| author_facet | Guo Qiaoping Meng Wei |
| author_sort | Guo Qiaoping |
| collection | DOAJ |
| description | Gutin and Rafiey [Multipartite tournaments with small number of cycles, Australas J. Combin. 34 (2006) 17–21] raised the following two problems: (1) Let m ∈ {3, 4, . . ., n}. Find a characterization of strong n-partite tournaments having exactly n − m + 1 cycles of length m; (2) Let 3 ≤ m ≤ n and n ≥ 4. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n − m + 1 cycles of length m for two values of m? In this paper, we discuss the strong n-partite tournaments D containing exactly n − m + 1 cycles of length m for 4 ≤ m ≤ n − 1. We describe the substructure of such D satisfying a given condition and we also show that, under this condition, the second problem has a negative answer. |
| first_indexed | 2024-03-12T07:32:41Z |
| format | Article |
| id | doaj.art-d214e05c4ed142749f5e32bbd2507d78 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T07:32:41Z |
| publishDate | 2021-02-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-d214e05c4ed142749f5e32bbd2507d782023-09-02T21:42:49ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922021-02-01411758210.7151/dmgt.2167dmgt.2167On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length mGuo Qiaoping0Meng Wei1School of Mathematical Sciences, Shanxi University, Taiyuan, 030006, ChinaSchool of Mathematical Sciences, Shanxi University, Taiyuan, 030006, ChinaGutin and Rafiey [Multipartite tournaments with small number of cycles, Australas J. Combin. 34 (2006) 17–21] raised the following two problems: (1) Let m ∈ {3, 4, . . ., n}. Find a characterization of strong n-partite tournaments having exactly n − m + 1 cycles of length m; (2) Let 3 ≤ m ≤ n and n ≥ 4. Are there strong n-partite tournaments, which are not themselves tournaments, with exactly n − m + 1 cycles of length m for two values of m? In this paper, we discuss the strong n-partite tournaments D containing exactly n − m + 1 cycles of length m for 4 ≤ m ≤ n − 1. We describe the substructure of such D satisfying a given condition and we also show that, under this condition, the second problem has a negative answer.https://doi.org/10.7151/dmgt.2167multipartite tournamentstournamentscycles05c2005c38 |
| spellingShingle | Guo Qiaoping Meng Wei On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m Discussiones Mathematicae Graph Theory multipartite tournaments tournaments cycles 05c20 05c38 |
| title | On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m |
| title_full | On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m |
| title_fullStr | On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m |
| title_full_unstemmed | On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m |
| title_short | On the n-Partite Tournaments with Exactly n − m + 1 Cycles of Length m |
| title_sort | on the n partite tournaments with exactly n m 1 cycles of length m |
| topic | multipartite tournaments tournaments cycles 05c20 05c38 |
| url | https://doi.org/10.7151/dmgt.2167 |
| work_keys_str_mv | AT guoqiaoping onthenpartitetournamentswithexactlynm1cyclesoflengthm AT mengwei onthenpartitetournamentswithexactlynm1cyclesoflengthm |