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Facial Achromatic Number Of Triangulations With Given Guarding Number, Naoki Matsumoto, Yumiko Ohno
Facial Achromatic Number Of Triangulations With Given Guarding Number, Naoki Matsumoto, Yumiko Ohno
Theory and Applications of Graphs
A (not necessarily proper) k-coloring c : V(G) → {1,2,…k} of a graph G on a surface is a facial t-complete k-coloring if every t-tuple of colors appears on the boundary of some face of G. The maximum number k such that G has a facial t-complete k-coloring is called a facial t-achromatic number of G, denoted by ψt(G). In this paper, we investigate the relation between the facial 3-achromatic number and guarding number of triangulations on a surface, where a guarding number of a graph G embedded on a surface, …