Abstract
In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without i-circuits for 4 ≤ i ≤ 11 − 3σ is 3-choosable, that offers a new upper bound to a question of Y. Zhao.
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Xu, B.G., Lu, X.X. A structural theorem on embedded graphs and its application to colorings. Acta. Math. Sin.-English Ser. 25, 47–50 (2009). https://doi.org/10.1007/s10114-008-7011-9
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DOI: https://doi.org/10.1007/s10114-008-7011-9