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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Graphs and Combinato...arrow_drop_down
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Graphs and Combinatorics
Article . 2001 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Article . 2001
Data sources: DBLP
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Article . 2001
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On the Volume of 5-Cycle Trades

On the volume of 5-cycle trades
Authors: Maenhaut, B. M.;

On the Volume of 5-Cycle Trades

Abstract

The author investigates sufficient conditions for the existence of a 5-cycle trade of volume \(t\) and foundation \(v.\) This interesting survey includes recent results on volumes of 5-cycle trades. It is a continuation of articles by \textit{A. Rosa} [Cas. Pestovni Mat. 91, 53-62 (1966; Zbl 0151.33501)], by \textit{A. Rosa} and \textit{S. Znám} [Discrete Math. 128, No. 1-3, 305-316 (1994; Zbl 0797.05063)] and by \textit{D. E. Bryant} [Australas. J. Comb. 15, 161-176 (1997; Zbl 0880.05017)]. A 5-cycle trade of volume \(t\) is a graph \(G\) whose edge set can be partitioned into \(t\) 5-cycles in at least two ways, such that the two collections of 5-cycles have no 5-cycles in common. The foundation \(v\) of a trade is the number of distinct vertices occurring in the graph \(G.\) Let \(E(v)\) be the set of all \(t\) such that there exists a 5-cycle trade of volume \(t\) with foundation \(v\) and let \(P(v)\) be the set of the possible volumes for a 5-cycle trade on \(v\) vertices. The author proves that, for all non-negative integers \(v\), \(E(v) = P(v).\) Tables of upper and lower bounds on the volume of a 5-cycle trade on \(v\) vertices and large, small and middle trade volumes are given.

Country
Australia
Related Organizations
Keywords

230100 Mathematics, foundation of a trade, volume of a trade, C1, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), 5-cycle, 5-cycle trade, Paths and cycles, Mathematics

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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!
5
Average
Top 10%
Average
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