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Article . 2011
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Discrete Mathematics Algorithms and Applications
Article . 2011 . Peer-reviewed
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Article . 2011
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https://dx.doi.org/10.1142/s17...
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CYCLES IN TRIANGLE-FREE GRAPHS

Cycles in triangle-free graphs
descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 2011 English Publisher:World Scientific Pub Co Pte LtJournal:Discrete Mathematics, Algorithms and Applications, volume 3, pages 343-356 (issn: 1793-8309, eissn: 1793-8317, Copyright policy )
Authors: Xiaojuan Li; Bing Wei 0001; Yongjin Zhu;

doi: 10.1142/s1793830911001267

CYCLES IN TRIANGLE-FREE GRAPHS

Abstract

Let G be a k-connected (k ≥ 3), triangle-free graph with α(G) ≤ k + 1. If G is not Petersen graph and G ∉ {Kk, k, Kk, k + 1, Kk + 1, k+1}, then G contains cycles of lengths from 4 to |V(G)|. This generalizes a result conjectured by Amar et al. (Graphs Combin.7 (1991)) and proved by Lou (Discrete Math.152 (1996)).

Related Organizations
Keywords

Connectivity, Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.), triangle-free graph, cycles, independence number, Paths and cycles

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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