A map coloring problem

Abstract

In Chaps. 2 and 3, we considered certain vertex colorings induced by edge colorings of a graph; while in Chaps. 4 and 5, we considered certain edge colorings induced by vertex colorings. Proper vertex colorings of graphs and the chromatic number of a graph originated from interest in map colorings. Other vertex colorings were also suggested from map colorings, which induced proper vertex colorings of graphs that often required using fewer colors than the chromatic number of a graph. In this chapter, we describe four such proper colorings originating from map colorings. These four vertex colorings will then be discussed in more detail in Chaps. 7–10.