科研之友
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摘要
A k-chromatic graph G is uniquely k-colorable if G has only one k-coloring up to permutation of the colors. In this paper, we focus on uniquely k-colorable graphs on surfaces. Let F-2 be a closed surface except the sphere, and let chi(F-2) be the maximum number of the chromatic number of graphs which can be embedded on F-2. Then we shall prove that the number of uniquely k-colorable graphs on F-2 is finite if k %26gt;= 5, and we characterize uniquely chi(F-2)-colorable graphs on F-2. Moreover, we completely determine uniquely k-colorable graphs on the projective plane, where k %26gt;= 5.
- 出版日期2014-4
