Journal of East China Normal University(Natural Sc ›› 2014, Vol. 2014 ›› Issue (3): 40-44.

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List edge and list total coloring of triangle-free 1-planar graphs

SONG Wen-yao,  MIAO Lian-ying,  ZHANG Shu-jie   

  1. College of Sciences, China University of Mining and Technology,  Xuzhou Jiangsu 221016, China
  • Received:2013-05-01 Revised:2013-08-01 Online:2014-05-25 Published:2014-07-25

Abstract: A graph is 1-planar if it can be drawn on the plane so that
each edge is crossed by at most one other edge. In this paper, it
was proved that every triangle-free 1-planar graph $G$ with maximum
degree $\Delta\geqslant15$ can be $\Delta$-edge-choosable and
($\Delta$+1)-total -choosable.

Key words: 1-planar, discharging method, maximum degree, choosability

CLC Number: