Proper Circular-arc Graphs Research Articles

The NP-Completeness of Edge-Coloring

We show that it is NP-complete to determine the chromatic index of an arbitrary graph. The problem remains NP-complete even for cubic graphs.

An $O(n^2 )$ Algorithm for Coloring Proper Circular Arc Graphs

A graph is a circular arc graph if each vertex of the graph is associated with an arc on a circle in such a way that two vertices of the graph are adjacent if and only if the corresponding arcs overlap. A circular arc graph is proper if none of the representing arcs is contained within another. An $O(n^2 )$ algorithm is given for determining whether a proper circular arc graph with n nodes may be colored with k colors.

Structure theorems for some circular-arc graphs

A proper circular-arc graph is a graph that has an intersection model formed by a family of overlapping arcs on some circle in which no arc contains another. A unit circular-arc graph is a graph that has an intersection model formed by a family of unit-length arcs on some circle. This paper gives structure theorems for proper circular-arc graphs and for unit circular-arc graphs.