Vertex-Disjoint Cycles Containing Specified Edges

Egawa, Yoshimi; Faudree, Ralph J.; Győri, Ervin; Ishigami, Yoshiyasu; Schelp, R. H.; Wang, Hong

doi:10.1007/s003730050005

Cited by 46 publications

(24 citation statements)

References 2 publications

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“…In fact, Egawa et al [1] obtained a very similar result earlier in a bit different setting. In [8], we proved that the degree condition can be weakened if H has minimum degree at least two.…”

Section: A Graph G Is H-linked If Every Injective Mapping F : V (H ) supporting

confidence: 68%

Minimum degree conditions for H-linked graphs

Kostochka

Yu²

2005

Electronic Notes in Discrete Mathematics

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Section: A Graph G Is H-linked If Every Injective Mapping F : V (H ) supporting

confidence: 68%

Minimum degree conditions for H-linked graphs

Kostochka

Yu²

2005

Electronic Notes in Discrete Mathematics

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“…. , C k covering all the vertices of G such that C i passes through e i for all 1 ≤ i ≤ k. This conjecture was confirmed and completely solved by Egawa, Faudree, Györi, Ishigami, Schelp and Wang in [4]. Here we propose the following conjecture:…”

Section: Introductionsupporting

confidence: 70%

Disjoint Cycles With Prescribed Lengths and Independent Edges in Graphs

Wang¹

2014

Journal of the Korean Mathematical Society

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Abstract. We conjecture that if k ≥ 2 is an integer and G is a graph of order n with minimum degree at least (n + 2k)/2, then for any k independent edges e 1 , . . . , e k in G and for any integer partition n = n 1 + · · · + n k with n i ≥ 4 (1 ≤ i ≤ k), G has k disjoint cycles C 1 , . . . , C k of orders n 1 , . . . , n k , respectively, such that C i passes through e i for all 1 ≤ i ≤ k. We show that this conjecture is true for the case k = 2. The minimum degree condition is sharp in general.

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“…From Egawa et al [7], we have that, for any edge, there is a hamilton cycle containing a specified edge but for several exceptions. Furthermore, Kaneko and Yoshimoto [10] showed that for any 2 k ðjVðGÞj À 1Þ=4, we can find a 2-factor with k cycles containing a specified edge except for a simple exception.…”

Section: B 2-factorsmentioning

confidence: 98%