On structure of graphs embedded on surfaces of nonnegative characteristic with application to choosability

Authors:
Baogang Xu
Affiliations:
Academy of Mathematics and Systems Science, Institute of Systems Sciences, CAS, Zhongguancun, Beijing, 100080, People's Republic of China
Venue:
Discrete Mathematics
Year:
2002

Citing 13
Cited 1

Contractible edges in 3-connected graphs

Journal of Combinatorial Theory Series B
List colourings of planar graphs

Discrete Mathematics
Every planar graph is 5-choosable

Journal of Combinatorial Theory Series B
The list chromatic index of a bipartite multigraph

Journal of Combinatorial Theory Series B
A new proof of the 6 color theorem

Journal of Graph Theory
3-list-coloring planar graphs of girth 5

Journal of Combinatorial Theory Series B
A not 3-choosable planar graph without 3-cycles

Discrete Mathematics
Every 2-choosable graph is (2m, m)-choosable

Journal of Graph Theory
Cyclic degree and cyclic coloring of 3-polytopes

Journal of Graph Theory
On 3-colorable non-4-choosable planar graphs

Journal of Graph Theory
On vertex types and cyclic colourings of 3-connected plane graphs

Discrete Mathematics
On structure of some plane graphs with application to choosability

Journal of Combinatorial Theory Series B
Graph Theory With Applications

Graph Theory With Applications

Every toroidal graph without adjacent triangles is (4, 1)*-choosable

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

In this paper, we prove a structural theorem of Lebesgue's type concerning some unavoidable configurations for graphs which can be embedded on surfaces of nonnegative characteristic and in which no two 3-cycles share a common vertex. As a corollary, we get a result about choosability of graphs embedded in surface of positive characteristic.