Interval Completion with the Smallest Max-Degree

(Extended Abstract)
  • Fedor V. Fomin
  • Petr A. Golovach
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1517)


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 G2 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 G2 minus one. Finally, we show that there is a polynomial time algorithm for computing the interval degree of AT-free claw-free graphs.


Interval Graph Chordal Graph Minimal Separator Left Graph Clique Number 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Fedor V. Fomin
    • 1
  • Petr A. Golovach
    • 2
  1. 1.Department of Operations Research, Faculty of Mathematics and MechanicsSt.Petersburg State UniversitySt.PetersburgRussia
  2. 2.Department of Applied Mathematics, Faculty of MathematicsSyktyvkar State UniversitySyktyvkarRussia

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