Bounds on Maximum Weight Directed Cut
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| Název: | Bounds on Maximum Weight Directed Cut |
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| Autoři: | Ai, Jiangdong, Gerke, Stefanie, Gutin, Gregory, Yeo, Anders, Zhou, Yacong |
| Zdroj: | SIAM Journal on Discrete Mathematics. 38:2370-2391 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Society for Industrial & Applied Mathematics (SIAM), 2024. |
| Rok vydání: | 2024 |
| Témata: | FOS: Computer and information sciences, weighted digraph, Discrete Mathematics (cs.DM), acyclic digraph, FOS: Mathematics, Mathematics - Combinatorics, directed cut, 0102 computer and information sciences, Combinatorics (math.CO), 0101 mathematics, 01 natural sciences, Computer Science - Discrete Mathematics |
| Popis: | We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobas, Gyafas, Lehel and Scott (J Graph Th 55(1) (2007)) for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems. |
| Druh dokumentu: | Article |
| Jazyk: | English |
| ISSN: | 1095-7146 0895-4801 |
| DOI: | 10.1137/23m1567394 |
| DOI: | 10.48550/arxiv.2304.10202 |
| Přístupová URL adresa: | http://arxiv.org/abs/2304.10202 |
| Rights: | CC BY |
| Přístupové číslo: | edsair.doi.dedup.....16f1e3c67e8a1a1dc013ecf834c25a1c |
| Databáze: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | We obtain lower and upper bounds for the maximum weight of a directed cut in the classes of weighted digraphs and weighted acyclic digraphs as well as in some of their subclasses. We compare our results with those obtained for the maximum size of a directed cut in unweighted digraphs. In particular, we show that a lower bound obtained by Alon, Bollobas, Gyafas, Lehel and Scott (J Graph Th 55(1) (2007)) for unweighted acyclic digraphs can be extended to weighted digraphs with the maximum length of a cycle being bounded by a constant and the weight of every arc being at least one. We state a number of open problems. |
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| ISSN: | 10957146 08954801 |
| DOI: | 10.1137/23m1567394 |