Decompositions and Reductions of Snarks

Journal of Graph Theory

Volumn 22, Issue 3, 1996, Pages 253-279

  Nedela, Roman ^a   Škoviera, Martin ^b  

^a MATEJ BEL UNIVERSITY   (Slovakia)

^b Physics and Informatics   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030548383     PISSN: 03649024     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0118(199607)22:3<253::AID-JGT6>3.0.CO;2-L     Document Type: Article

References (26)

1. G. M. Adelson-Velskii and V. K. Titov, On edge 4-chromatic cubic graphs. Voprosy kibernetiki 1 (1973) 5-14 (in Russian).
2. D. Blanuša, Problem četiriju boja (The four-color problem]. Glasnik Mat. Fiz. Astr. Ser. II (Hrvatsko Prisodoslovno Društvo) 1 (1946) 31-42 (in Croatian).
3. P. J. Cameron, A. G. Chetwynd, and J. J. Watkins, Decomposition of snarks. J. Graph Theory 11 (1987) 13-19.
4. U. A. Celmins and E. R. Swart, The construction of snarks. Research Report CORR 79-18, University of Waterloo, Waterloo (1979).
5. A. G. Chetwynd and R. J. Wilson, Snarks and supersnarks. The Theory and Application of Graphs. Wiley, New York (1981) 215-241.
6. B. Descartes, Network colourings. Math. Gazette 32 (1948) 67-69.
7. M. A. Fiol, A Boolean algebra approach to the construction of snarks. Graph Theory, Combinatorics and Applications, Vol. 1. Addison-Wesley, Reading, MA (1991) 493-524.
8. S. Fiorini and R. J. Wilson, Edge-Colourings of Graphs, Research Notes in Math., Vol. 16, Pitman, London (1977).
9. J.-L. Fouquet, Note sur la non existence d'un snark d'ordre 16. Discrete Math. 38 (1982) 163-171.
10. M. Gardner, Mathematical games: Snarks, boojums and other conjectures related to the four-color-map theorem. Sci. Am. 234 (1976) 126-130.
11. M. K. Goldberg, Construction of class 2 graphs with maximum vertex degree 3. J. Combinat. Theory Ser. B 31 (1981) 282-291.
12. A. Huck, On cycle-double-covers of some graphs. Preprint.
13. A. Huck and M. Kochol, Five cycle double covers of some cubic graphs. J. Combinat. Theory Ser. B 64 (1995) 119-125.
14. R. Isaacs, Infinite families of non-trivial trivalent graphs which are not Tait colorable. Am. Math. Month. 82 (1975) 221-239.
15. F. Jaeger, A survey of the Cycle Double Conjecture. Ann. Discrete Math. 26 (1985) 1-12.
16. F. Jaeger and T. Swart, Problem session. Ann. Discrete Math. 9 (1980) 305.
17. M. Kochol, A cyclically 6-connected snark of order 118. Discrete Math. To appear.
18. M. Kochol, Snarks without small cycles. J. Combinat. Theory Ser. B. Accepted.
19. M. Kochol and M. Škoviera, Superposition of graphs with no nowhere-zero k-flows. In progress.
20. L. Lovász, On graphs containing no independent cycles. Mat. Lapok 16 (1965) 289-299 (Hungarian).
21. R. Nedela and M. Škoviera, Constructions of irreducible reducible snarks. In progress.
22. M. Preissmann, C-minimal snarks. Ann. Discrete Math. 17 (1983) 559-565.
23. E. Steffen, Classifications and characterisations of snarks. SFB Preprint, Universität Bielefeld, Bielefeld (1994).
24. P. G. Tait, Remarks on the colouring of maps. Proc. Roy. Soc. Edinburgh 10 (1880) 729.
25. J. J. Watkins, Snarks. Ann. NY Acad. Sci. 576 (1989) 606-622.
26. J. J. Watkins and R. J. Wilson, A survey of snarks. Graph Theory, Combinatorics, and Applications Vol. 2 Wiley, New York (1991) 1129-1144.