Quartet compatibility and the quartet graph.
Cyclically 5-edge connected non-bicritical critical snarks
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].
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