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Cycles of length 0 modulo k in directed graphs

โœ 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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๐Ÿ“œ SIMILAR VOLUMES


Cycles of length 0 modulo 4 in graphs
โœ Nathaniel Dean; Linda Lesniak; Akira Saito ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 829 KB

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

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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

Cycles of even lengths modulo k
โœ Ajit A. Diwan ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 84 KB

## Abstract Thomassen [J Graph Theory 7 (1983), 261โ€“271] 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

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โœ J.A Bondy; M Simonovits ๐Ÿ“‚ Article ๐Ÿ“… 1974 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 363 KB
Cycles of given length in some K1,3-free
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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