Discussiones
Mathematicae Graph Theory 19(1) (1999) 5-11
DOI: https://doi.org/10.7151/dmgt.1081
CYCLICALLY 5-EDGE CONNECTED NON-BICRITICAL CRITICAL SNARKS
Stefan Grünewald Universität Bielefeld, Fakultät für Mathematik |
Eckhard Steffen Princeton University |
Abstract
Snarks are bridgeless cubic graphs with chromatic index χ′ = 4. A snark G is called critical if χ′(G-{v,w}) = 3, for any two adjacent vertices v and w.
For any k ≥ 2 we construct cyclically 5-edge connected critical snarks G having an independent set I of at least k vertices such that χ′(G-I) = 4.
For k = 2 this solves a problem of Nedela and Skoviera [6].
Keywords: cubic graphs, snarks, edge colorings.
1991 Mathematics Subject Classification: 05C15, 05C70.
References
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Received 24 November 1997
Revised 21 December 1998
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