A Structural Theorem on Embedded Graphs and Its Application to Colorings

作者:Xu Bao Gang*; Lu Xiao Xu
来源:Acta Mathematica Sinica-English Series, 2009, 25(1): 47-50.
DOI:10.1007/s10114-008-7011-9

摘要

In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic sigma <= 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 <= 11-3 sigma is 3-choosable, that offers a new upper bound to a question of Y. Zhao.