The restricted arc

An arc-representation of a graph is a function mapping each vertex in the graph to an arc on the unit circle in such a way that adjacent vertices are mapped to intersecting arcs. The width of such a representation is the maximum number of arcs passing through a single point. The arc-width of a graph is defined to be the minimum width over all of its arc-representations. We extend the work of Bar´at and Hajnal on this subject and develop a generalization we call restricted arcwidth.

18p thulanh5 12-09-2011 60 4   Download