Abstract
The interval degree of a graph is defined to be the smallest max-degree of any of its interval supergraphs. We find various bounds for this parameter. We prove that for any graph G the interval degree of G is at least the bandwidth of G, the pathwidth of G 2 and at most twice the bandwidth of G. Also we show that if G is an AT-free claw-free graph, then the interval degree of G is equal to the clique number of G 2 minus one. Finally, we show that there is a polynomial time algorithm for computing the interval degree of AT-free claw-free graphs.
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Fomin, F.V., Golovach, P.A. (1998). Interval Completion with the Smallest Max-Degree. In: Hromkovič, J., Sýkora, O. (eds) Graph-Theoretic Concepts in Computer Science. WG 1998. Lecture Notes in Computer Science, vol 1517. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10692760_29
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DOI: https://doi.org/10.1007/10692760_29
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