κ-path-connectivity and mk-generation: an Upper Bound on m

Abreu, M.; Locke, S. C.

doi:10.1007/978-3-7643-7400-6_2

κ-path-connectivity and mk-generation: an Upper Bound on m

M. Abreu⁴ &
S. C. Locke⁵

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Abstract

We consider simple connected graphs for which there is a path of length at least κ between every pair of distinct vertices. We wish to show that in these graphs the cycle space over ℤ₂ is generated by the cycles of length at least mk, where m = 1 for 3 ≤ κ ≤ 6, m = 6/7 for κ = 7, m ≥ 1/2 for κ ≥ 8 and m ≤ 3/4 +o(1) for large k.

The authors would like to thank the ‘Equipe Combinatoire’ Paris 6 and CNRS for the generous support to attend GT04 conference.

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References

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Authors and Affiliations

Dipartimento di Matematica, Università degli Studi della Basilicata, Potenza, Italy
M. Abreu
Department of Mathematical Sciences, Florida Atlantic University, Florida, USA
S. C. Locke

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M. Abreu
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S. C. Locke
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Editors and Affiliations

Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622, Villeurbanne cedex, France
Adrian Bondy
Equipe Combinatoire et Optimisation Case 189, Université Pierre et Marie Curie, Paris 6, 75252, Paris Cedex 05, France
Jean Fonlupt , Jean-Claude Fournier & Jorge L. Ramírez Alfonsín , &
Laboratoire d’Informatique Fondamentale d’Orléans, Bâtiment IIIA, Rue Léonard de Vinci, B.P. 6759, 45067, Orléans Cedex 2, France
Jean-Luc Fouquet

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Abreu, M., Locke, S.C. (2006). κ-path-connectivity and mk-generation: an Upper Bound on m . In: Bondy, A., Fonlupt, J., Fouquet, JL., Fournier, JC., Ramírez Alfonsín, J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7400-6_2

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DOI: https://doi.org/10.1007/978-3-7643-7400-6_2
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7228-6
Online ISBN: 978-3-7643-7400-6
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