摘要
In 2003, Borodin and Raspaud proved that if G is a plane graph without 5-circuits and without triangles of distance less than four, then G is 3-colorable. In this paper, we prove that if G is a plane graph without 5- and 6-circuits and without triangles of distance less than 2, then G is 3-colorable.
In 2003, Borodin and Raspaud proved that if G is a plane graph without 5-circuits and without triangles of distance less than four, then G is 3-colorable. In this paper, we prove that if G is a plane graph without 5- and 6-circuits and without triangles of distance less than 2, then G is 3-colorable.
基金
Supported by National Natural Science Foundation of China(No.10931003 and 11171160)
the Doctoral Fund of Ministry of Education of China
