文摘
A Grünbaum coloring of a triangulation G on a surface is a 3-edge coloring of G such that each face of G receives three distinct colors on its boundary edges. In this paper, we prove that every Fisk triangulation on the projective plane bbbcb8b768cf8891ea7ac6b95" title="Click to view the MathML source">P has a Grünbaum coloring, where a “Fisk triangulation” is one with exactly two odd degree vertices such that the two odd vertices are adjacent. To prove the theorem, we establish a generating theorem for Fisk triangulations on bbbcb8b768cf8891ea7ac6b95" title="Click to view the MathML source">P. Moreover, we show that a triangulation G on bbbcb8b768cf8891ea7ac6b95" title="Click to view the MathML source">P has a Grünbaum coloring with each color-induced subgraph connected if and only if every vertex of G has even degree.