On partitioning interval and circular-arc graphs into proper interval subgraphs with applications

Abstract

In this note, we establish that any interval or circular-arc graph with n vertices admits a partition into O(log n) proper interval subgraphs. This bound is shown to be asymptotically sharp for an infinite family of interval graphs. Moreover, the constructive proof yields a linear-time and space algorithm to compute such a partition. The second part of the paper is devoted to an application of this result, which has actually inspired this research: the design of an efficient approximation algorithm for a NP-hard problem of planning working schedules. © Springer-Verlag 2004.