ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

13. Combinatorics

1991 MS Classification: 5 Kochol, Martin, Slovak Academy of Sciences, Slovakia Superposition – a method for constructing graphs without nowhere-zero k-flows A graph admits a nowhere-zero k-flow if its edges can be oriented and assigned by values ±1, …, ±(k − 1) so that the sum of the incoming values equals to the sum of the outcoming ones for every vertex of the graph. We present a new method for constructing graphs without nowhere-zero k-flows. We apply it for constructions of snarks with arbitrary large girth and several new results about nowhere-zero flow problems. Reference: M. Kochol, Snarks without small cycles, J. Combin. Theory Ser. B 67 (1996), 34-47.