Facial visibility in edge colored plane graphs
The paper studies facial edge-coloring of plane graphs. A facial edge-coloring of a plane graph \(G\) is an edge-coloring that is proper on the edges of the boundary walks of its faces. A face \(f\) sees \(p\) colors, if the edges of its boundary walk are colored with \(p\) distinct colors. The facial edge-\(p\)-visibility number of a plane graph \(G\) is the maximum number \(k\) of colors such that there is a facial \(k\)-edge-coloring of \(G\) and each face of \(G\) sees at most \(p\) colors. The authors prove several general tight lower and upper bounds for this graph coloring invariant. Moreover, they determine the exact values for certain special families of plane graphs.
scientific article; zbMATH DE number 7451438
scientific article