On the Connection Between the Chromatic Number of a Graph and the Number of Cycles Covering a Vertex or an Edge
- Авторы: Berlov S.1, Tyschuk K.1
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Учреждения:
- Physics and Mathematics Lyceum 239
- Выпуск: Том 232, № 1 (2018)
- Страницы: 1-5
- Раздел: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/241246
- DOI: https://doi.org/10.1007/s10958-018-3853-6
- ID: 241246
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Аннотация
We prove several tight bounds on the chromatic number of a graph in terms of the minimum number of simple cycles covering a vertex or an edge of this graph. Namely, we prove that X(G) ≤ k in the following two cases: any edge of G is covered by less than [e(k − 1) ! − 1] simple cycles, or any vertex of G is covered by less than \( \left[\frac{ek!}{2}-\frac{k+1}{2}\right] \) simple cycles. Tight bounds on the number of simple cycles covering an edge or a vertex of a k-critical graph are also proved.
Об авторах
S. Berlov
Physics and Mathematics Lyceum 239
Автор, ответственный за переписку.
Email: sberlov@rambler.ru
Россия, St.Petersburg
K. Tyschuk
Physics and Mathematics Lyceum 239
Email: sberlov@rambler.ru
Россия, St.Petersburg