DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 18(2) (1998) 147-158
DOI: 10.7151/dmgt.1070

ON GENERATING SNARKS

Busiso P. Chisala

Department of Mathematical Sciences, Chancellor College
P.O. Box 280, Zomba, Malawi

Abstract

We discuss the construction of snarks (that is, cyclically 4-edge connected cubic graphs of girth at least five which are not 3-edge colourable) by using what we call colourable snark units and a welding process.

Keywords: snarks, cubic graphs, sirth, edge colouring.

1991 Mathematics Subject Classification: 05C15.

References

[1] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, 1976).
[2] B. Jackson, On cycle Covers, cycle Decompositions and Euler Tours of Graphs, Preprint (1993).
[3] F. Jaeger, Nowhere-zero Flow Problems, in: Graph Theory 3, edited by L.W, Beincke and R.J. Wilson (Academic Press Ltd., New York, 1988).
[4] R. Isaacs, Infinite families of non-trivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly 82 (1975) 221-239, doi: 10.2307/2319844.
[5] J.J. Watkins and R.J. Wilson, A Survey of snarks, in: Graph Theory, Combinatorics and Applications, Vol. 2, Proceedings of the Sixth Quadrennial International Conference on the Theory and Applications of Graphs, Y. Alavi et. al. (eds) (John Wiley & Sons, 1991) 1129-1144.

Received 22 August 1997
Revised 2 May 1998