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The only open case of Vizing’s conjecture that every planar graph with Δ≥6 is a class 1 graph is Δ=6. We give a short proof of the following statement: there is no 6-critical plane graph G, such that every vertex of G is incident to at most three 3-faces. A stronger statement without restriction to critical graphs is stated in Wang and Xu (2013). However, the proof given there works only for critical...
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