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 \(\mathcal{NP}\)-hard problem of planning working schedules.
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Gardi, F. (2004). On Partitioning Interval and Circular-Arc Graphs into Proper Interval Subgraphs with Applications. In: Farach-Colton, M. (eds) LATIN 2004: Theoretical Informatics. LATIN 2004. Lecture Notes in Computer Science, vol 2976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24698-5_17
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DOI: https://doi.org/10.1007/978-3-540-24698-5_17
Publisher Name: Springer, Berlin, Heidelberg
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