Отправить статью по E-mail New Cases of the Polynomial Solvability of the Independent Set Problem for Graphs with Forbidden Paths
- Авторы: Alekseev V.E.1, Sorochan S.V.1
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Учреждения:
- Institute of Information Technology, Mathematics and Mechanics
- Выпуск: Том 12, № 2 (2018)
- Страницы: 213-219
- Раздел: Article
- URL: https://journals.rcsi.science/1990-4789/article/view/213041
- DOI: https://doi.org/10.1134/S1990478918020023
- ID: 213041
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Аннотация
The independent set problem is solvable in polynomial time for the graphs not containing the path Pk for any fixed k. If the induced path Pk is forbidden then the complexity of this problem is unknown for k > 6. We consider the intermediate cases that the induced path Pk and some of its spanning supergraphs are forbidden. We prove the solvability of the independent set problem in polynomial time for the following cases: (1) the supergraphs whose minimal degree is less than k/2 are forbidden; (2) the supergraphs whose complementary graph has more than k/2 edges are forbidden; (3) the supergraphs from which we can obtain Pk by means of graph intersection are forbidden.
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Об авторах
V. Alekseev
Institute of Information Technology, Mathematics and Mechanics
Автор, ответственный за переписку.
Email: aleve@rambler.ru
Россия, pr. Gagarina 23, Nizhny Novgorod, 603950
S. Sorochan
Institute of Information Technology, Mathematics and Mechanics
Email: aleve@rambler.ru
Россия, pr. Gagarina 23, Nizhny Novgorod, 603950
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