Szczegóły publikacji
Opis bibliograficzny
Cycle lengths in graphs of given minimum degree / Yandong Bai, Andrzej Grzesik, Binlong Li, Magdalena PROROK // Journal of Combinatorial Theory . Series B ; ISSN 0095-8956. — 2026 — vol. 180, s. 111–150. — Bibliogr. s. 150, Abstr. — Publikacja dostępna online od: 2026-07-09
Autorzy (4)
- Bai Yandong
- Grzesik Andrzej
- Li Binlong
- AGHProrok Magdalena
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 169232 |
|---|---|
| Data dodania do BaDAP | 2026-07-31 |
| Tekst źródłowy | URL |
| DOI | 10.1016/j.jctb.2026.06.003 |
| Rok publikacji | 2026 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Czasopismo/seria | Journal of Combinatorial Theory, Series B |
Abstract
We prove that if G is a 2-connected graph with minimum degree at least k⩾4, then (1) G contains k cycles whose lengths form an arithmetic progression with common difference one or two, unless G≅Kk+1 or Kk,n−k; (2) G contains cycles of lengths ℓ modulo k for all even ℓ, unless G≅Kk+1 or Kk,n−k; (3) G contains cycles of lengths ℓ modulo k for all ℓ, unless G≅Kk+1 or G is bipartite. In addition, we show that if k is even and G is 2-connected with minimum degree at least k−1 and order at least k+2, then G contains cycles of lengths ℓ modulo k for all even ℓ. As a corollary, we determine the maximum number of edges in a graph without a cycle of length divisible by k for all odd k.
