A sufficient condition for all short cycles

Brandt, Stephan

doi:10.1016/s0166-218x(97)00032-2

Cited by 39 publications

(24 citation statements)

References 3 publications

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“…In [69], Brandt generalized Theorem 4.10 and showed that the same size without the hamiltonicity requirement is sufficient for a graph to be weakly pancyclic with girth 3.…”

Section: Weakly Pancyclic Graphsmentioning

confidence: 99%

Cycles in graphs and related problems

Marczyk

2008

Dissertationes Math.

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“…In [69], Brandt generalized Theorem 4.10 and showed that the same size without the hamiltonicity requirement is sufficient for a graph to be weakly pancyclic with girth 3.…”

Section: Weakly Pancyclic Graphsmentioning

confidence: 99%

Cycles in graphs and related problems

Marczyk

2008

Dissertationes Math.

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“…[2,[5][6][7]). Suppose G is a graph with girth gðGÞ and circumference cðGÞ: An interval ½a; b of integers with gðGÞ a b cðGÞ is said to be a domain of pancyclicity of G if for every t with a t b there is a cycle C t 2 G:…”

Section: Domains Of Pancyclicitymentioning

confidence: 99%

Cycles and paths in graphs with large minimal degree

Nikiforov

Schelp

2004

Journal of Graph Theory

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Let G be a simple graph of order n and minimal degree > cn (0 < c < 1=2). We prove that (1) There exist n 0 ¼ n 0 (c) and k ¼ k(c) such that if n > n 0 and G contains a cycle C t for some t > 2k; then G contains a cycle C tÀ2s for some positive s < k; (2) Let G be 2-connected and nonbipartite. For each " (0 < " < 1), there exists n 0 ¼ n 0 (c; ") such that if n ! n 0 then G contains a cycle C t for all t with d

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“…Further, an additional goal is to characterize the extermal graphs G(n; F) where f (n; F) is attained. This problem has been studied extensively by a number of authors [4,5,7,8,9]. In 1998, Jia proved that …”

Section: Introductionmentioning

confidence: 99%