In several papers a variety of questions have been raised concerning the existence of cycles of length Omod k in graphs. For the case k=4, we answer three of these questions by showing that a graph G contains such a cycle provided it has any of the following three properties: (1) G has minimum degre
Cycles of length 0 modulo k in directed graphs
โ Scribed by Noga Alon; N Linial
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 417 KB
- Volume
- 47
- Category
- Article
- ISSN
- 0095-8956
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๐ SIMILAR VOLUMES
Saito, A., Cycles of length 2 modulo 3 in graphs, Discrete Mathematics 101 (1992) 285-289. We prove that if a graph G of minimum degree at least 3 has no cycle of length 2 (mod 3), then G has an induced subgraph which is isomorphic to either K4 or Ks,s. The above result together with its relatively
## Abstract Thomassen [J Graph Theory 7 (1983), 261โ271] conjectured that for all positive integers __k__ and __m__, every graph of minimum degree at least __k__+1 contains a cycle of length congruent to 2__m__ modulo __k__. We prove that this is true for __k__โฉพ2 if the minimum degree is at least 2
Let G be a non-trivial connected &,-free graph. If any vertex cut of G contains a veitex v such that G@!(u)) is connected, we prove that G is pancyclic. If G(Z+I(u)) is conaected for any vertex u of G, we prove that G is vertex pancyclic and obtain a polynomial time algorithm for constructing cycles