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- W2064033752 abstract "A snark is a “nontrivial” cubic graph whose edges cannot be properly coloured by three colours; it is irreducible if each nontrivial edge-cut divides the snark into colourable components. Irreducible snarks can be viewed as simplest uncolourable structures. In fact, all snarks can be composed from irreducible snarks in a suitable way. In this paper we deal with the problem of the existence of irreducible snarks of given order and cyclic connectivity. We determine all integers n for which there exists an irreducible snark of order n , and construct irreducible snarks with cyclic connectivity 4 and 5 of all possible orders. Moreover, we construct cyclically 6-connected irreducible snarks of each even order ⩾ 210 . (Cyclically 7-connected snarks are believed not to exist.)" @default.
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- W2064033752 date "2006-05-01" @default.
- W2064033752 modified "2023-09-29" @default.
- W2064033752 title "Irreducible snarks of given order and cyclic connectivity" @default.
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- W2064033752 doi "https://doi.org/10.1016/j.disc.2006.02.003" @default.
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