Názov:Small critical snarks and their generalizations
Vedúci:RNDr. Ján Mazák, PhD.
Kµúčové slová:snark, irreducible, critical, bicritical, strictly critical, cyclical connectivity, girth, Tait colouring, flow
Abstrakt:Snarks are non-trivial bridgeless cubic graphs that are not 3-edge-colourable. This thesis extends the analysis of the structure of small bicritical snarks by the same author to strictly critical snarks. This analysis divides examined snarks into several infinite classes. We show that if we impose additional requirements on construction blocks used in the described classes, we are able to prove that the resulting snark is critical or bicritical. Using appropriate snarks we construct infinite families of snarks with girth 6 and cyclic connectivity 5 or 6. Additionally, we construct all non-trivial snarks with girth 6, cyclic connectivity at most 5 and order 40.

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