FACE-WIDTH OF EMBEDDED GRAPHS
Bojan Mohar · Czech digital mathematics library · 1997
In their work on graph minors, Robertson and Seymour introduced the face-width (or representativity) as a measure of how densely a graph is embedded on a surface.The face-width of a graph embedded in S is the smallest number k such that S contains a noncontractible closed curve that intersects the graph in k points.We survey recent developments in the theory of embeddings of graphs in surfaces that concern this important invariant of embedded graphs.