Yokohama City University and Yokohama National University
Abstract
application/pdfLet ＄M＄ be a closed 2-manifold. A face coloring of a triangulation ＄T＄ of ＄M＄ is called a cyclic coloration if, for any vertex, the incident faces have different colors. Let ＄V(T)＄ denote the vertex set of ＄T＄ . We conjecture that there will be found a constant ＄C(M)＄ so that ＄|V(T)|+C(M) colors are enough for cyclic coloration of any triangulation ＄T＄ of ＄M＄. When ＄M＄ is not the projective plane, we conjecture that ＄|V(T)|＄ colors will suffice, whenever ＄T＄ is minimal with respect to the number of vertices. If this conjecture is true, the formula for the minimum number of vertices in a triangulation of a given 2-manifold with boundary is determined to have at most one gap.departmental bulletin pape
