Reduction of the 5-Flow Conjecture to cyclically 6-edge-connected snarks

Journal of Combinatorial Theory. Series B

Volumn 90, Issue 1, 2004, Pages 139-145

  Kochol, Martin ^a  

^a INSTITUTE OF CHEMISTRY   (Slovakia)

Author keywords

Cyclic edge connectivity; Girth; Nowhere zero 5 flow; Snark

Indexed keywords

EID: 0346499280     PISSN: 00958956     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0095-8956(03)00080-7     Document Type: Article

References (14)

1. U.A. Celmins, On cubic graphs that do not have an edge-3-colouring, Ph.D. Thesis, Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Canada, 1984.
2. R. Isaacs, Infinite families of nontrivial trivalent graphs which are not Tait colorable, Amer. Math. Monthly 82 (1975) 221-239.
3. F. Jaeger, Nowhere-zero flow problems, in: L.W. Beineke, R.J. Wilson (Eds.), Selected Topics in Graph Theory 3, Academic Press, New York, 1988, pp. 71-95.
4. F. Jaeger, T. Swart, Conjecture I, in: M. Deza, I.G. Rosenberg (Eds.), Combinatorics 79, Annals of Discrete Mathematics, Vol. 9, North-Holland, Amsterdam, 1980, p. 305.
5. M. Kochol, Constructions of cyclically 6-edge-connected snarks, Technical Report TR-II-SAS-07/93-05, Institute for Informatics, Slovak Academy of Sciences, Bratislava, Slovakia, 1993.
6. M. Kochol, Snarks without small cycles, J. Combin. Theory Ser. B 67 (1996) 34-47.
7. M. Kochol, A cyclically 6-edge-connected snark of order 118, Discrete Math. 161 (1996) 297-300.
8. M. Kochol, Hypothetical complexity of the nowhere-zero 5-flow problem, J. Graph Theory 28 (1998) 1-11.
9. M. Kochol, Cubic graphs without a Petersen minor have nowhere-zero 5-flows, Acta Math. Univ. Comenian. (N.S.) 68 (1999) 249-252.
10. M. Kochol, Forbidden subgraphs for the smallest counterexample to the 5-flow conjecture, preprint 9/2001, Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia (http://www.mat.savba.sk/preprints).
11. M. Kochol, Superposition and constructions of graphs without nowhere-zero k-flows, European J. Combin. 23 (2002) 281-306.
12. M. Kochol, Constructions of graphs without nowhere-zero flows from Boolean formulas, Ars Combin., to appear.
13. W.T. Tutte, A contribution to the theory of chromatic polynomials, Canad. J. Math. 6 (1954) 80-91.
14. W.T. Tutte, A class of Abelian groups, Canad. J. Math. 8 (1956) 13-28.