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We generalize a parity result of Fleishner and Stiebitz that being combined with Alon–Tarsi polynomial method allowed them to prove that a 4‐regular graph formed by a Hamiltonian cycle and several disjoint triangles is always 3‐choosable. Also we show how a version of polynomial method gives slightly more combinatorial information about colorings than direct application of Alon's Combinatorial Nullstellensatz.
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