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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].
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].
Słowa kluczowe
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
5-11
Opis fizyczny
Daty
wydano
1999
otrzymano
1997-11-24
poprawiono
1998-12-21
Twórcy
autor
- Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany
autor
- Princeton University, Program in Applied and Computational Mathematics, Fine Hall, Washington Road, Princeton, New Jersey 08544-1000, USA
Bibliografia
- [1] D. Blanusa, Problem ceteriju boja (The problem of four colors), Hrvatsko Prirodoslovno Drustvo Glasnik Math.-Fiz. Astr. Ser. II, 1 (1946) 31-42.
- [2] G. Brinkmann and E. Steffen, Snarks and Reducibility, Ars Combin. 50 (1998) 292-296.
- [3] P.J. Cameron, A.G. Chetwynd and J.J. Watkins, Decomposition of Snarks,J. Graph Theory 11 (1987) 13-19, doi: 10.1002/jgt.3190110104.
- [4] M.K. Goldberg, Construction of class 2 graphs with maximum vertex degree 3, J. Combin. Theory (B) 31 (1981) 282-291, doi: 10.1016/0095-8956(81)90030-7.
- [5] 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.
- [6] R. Nedela and M. Skoviera, Decompositions and Reductions of Snarks, J. Graph Theory 22 (1996) 253-279, doi: 10.1002/(SICI)1097-0118(199607)22:3<253::AID-JGT6>3.0.CO;2-L
- [7] M. Preissmann, C-minimal Snarks, Annals Discrete Math. 17 (1983) 559-565.
- [8] M. Skoviera, personal communication.
- [9] E. Steffen, Critical Non-bicritical Snarks, Graphs and Combinatorics (to appear).
- [10] E. Steffen, Classifications and Characterizations of Snarks, Discrete Math. 188 (1998) 183-203, doi: 10.1016/S0012-365X(97)00255-0.
- [11] E. Steffen, On bicritical Snarks, Math. Slovaca (to appear).
- [12] J.J. Watkins, Snarks, Ann. New York Acad. Sci. 576 (1989) 606-622, doi: 10.1111/j.1749-6632.1989.tb16441.x.
- [13] J.J. Watkins, R.J. Wilson, A Survey of Snarks, in: Y. Alavi et al. (eds.), Graph Theory, Combinatorics and Applications (Wiley, New York, 1991) 1129-1144.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1081