6-path-connectivity and 6-generation

We consider simple connected graphs for which there is a path of length at least 6 between every pair of distinct vertices. We wish to show that in these graphs the cycle space over Z 2 is generated by the cycles of length at least 6. Furthermore, we wish to generalize the result for k-path-connecte...

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Bibliographic Details
Published in:Discrete mathematics 2005-09, Vol.301 (1), p.20-27
Main Authors: Abreu, M., Labbate, D., Locke, S.C.
Format: Article
Language:English
Subjects:
Combinatorics
Combinatorics. Ordered structures
Cycle space
Exact sciences and technology
Graph theory
k-generation
k-path-connectivity
Mathematics
Sciences and techniques of general use
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Summary:We consider simple connected graphs for which there is a path of length at least 6 between every pair of distinct vertices. We wish to show that in these graphs the cycle space over Z 2 is generated by the cycles of length at least 6. Furthermore, we wish to generalize the result for k-path-connected graphs which contain a long cycle.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2003.03.002