论文信息 - A 3-color Theorem on Plane Graphs without 5-circuits

A 3-color Theorem on Plane Graphs without 5-circuits

AbstractIn this paper, we prove that every plane graph without 5-circuits and without triangles of distance less than 3 is 3-colorable. This improves the main result of Borodin and Raspaud [Borodin, O. V., Raspaud, A.: A sufficient condition for planar graphs to be 3-colorable. Journal of Combinatorial Theory, Ser. B, 88, 17–27 (2003)], and provides a new upper bound to their conjecture.

Baogang Xu | Bao Gang Xu

[1] R. Steinberg. The State of the Three Color Problem , 1993 .

[2] André Raspaud,et al. A sufficient condition for planar graphs to be 3-colorable , 2003, J. Comb. Theory, Ser. B.

[3] Bao-gang Xu. On 3-colorings of Plane Graphs , 2004 .

[4] Yue Zhao,et al. A note on the three color problem , 1995, Graphs Comb..

[5] Baogang Xu. On 3-colorable plane graphs without 5- and 7-cycles , 2006, J. Comb. Theory, Ser. B.

[6] André Raspaud,et al. Planar graphs without cycles of length from 4 to 7 are 3-colorable , 2005, J. Comb. Theory, Ser. B.

[7] Oleg V. Borodin,et al. Structural properties of plane graphs without adjacent triangles and an application to 3-colorings , 1996, J. Graph Theory.