منابع مشابه
Treelike Snarks
In this talk we present snarks whose edges cannot be covered by fewer than five perfect matchings. Esperet and Mazzuoccolo found an infinite family of such snarks, generalising an example provided by Hägglund. We construct another infinite family, arising from a generalisation in a different direction. The proof that this family has the requested property is computer-assisted. In addition, we p...
متن کاملPermutation snarks
A permutation snark is a cubic graph with no 3-edge-colouring that contains a 2-factor consisting of two induced circuits. In the talk we analyse the basic properties of permutation snarks, focusing on the structure of edge-cuts of size 4 and 5. As an application of our knowledge we provide rich families of cyclically 4edge-connected and 5-edge-connected permutation snarks of order 8n+2 for eac...
متن کاملFactorisation of Snarks
We develop a theory of factorisation of snarks — cubic graphs with edge-chromatic number 4 — based on the classical concept of the dot product. Our main concern are irreducible snarks, those where the removal of every nontrivial edge-cut yields a 3-edge-colourable graph. We show that if an irreducible snark can be expressed as a dot product of two smaller snarks, then both of them are irreducib...
متن کامل6-decomposition of Snarks
A snark is a cubic graph with no proper 3-edge-colouring. In 1996, Nedela and Škoviera proved the following theorem: LetG be a snark with an k-edge-cut, k ≥ 2, whose removal leaves two 3-edgecolourable componentsM and N . Then bothM and N can be completed to two snarks M̃ and Ñ of order not exceeding that of G by adding at most κ(k) vertices, where the number κ(k) only depends on k. The known va...
متن کاملNon-Bicritical Critical Snarks
Snarks are cubic graphs with chromatic index 0 = 4. A snark G is called critical if 0 (G?fv; wg) = 3 for any two adjacent vertices v and w, and it is called bicritical if 0 (G ? fv; wg) = 3 for any two vertices v and w. We construct innnite families of critical snarks which are not bicritical. This solves a problem stated by Nedela and Skoviera in 7].
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2021
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2020.103220