Sharp Bounds for the Oriented Diameters of Interval Graphs and 2-Connected Proper Interval Graphs

  • Jing Huang
  • Dong Ye
Conference paper

DOI: 10.1007/978-3-540-72588-6_58

Part of the Lecture Notes in Computer Science book series (LNCS, volume 4489)
Cite this paper as:
Huang J., Ye D. (2007) Sharp Bounds for the Oriented Diameters of Interval Graphs and 2-Connected Proper Interval Graphs. In: Shi Y., van Albada G.D., Dongarra J., Sloot P.M.A. (eds) Computational Science – ICCS 2007. ICCS 2007. Lecture Notes in Computer Science, vol 4489. Springer, Berlin, Heidelberg

Abstract

The diameter diam(H) of a (directed) graph H is the maximum value computed over the lengths of all shortest (directed) paths in H. Given a bridgeless connected graph G, the oriented diameter OD(G) is given by \(OD(G) = \mbox{min}\{diam(H):\ H\ \mbox{is\ an\ orientation\ of}\ G\}\). In this paper, we show that \(OD(G) \leq \lceil \frac{3}{2} diam(G) \rceil + 1\) for every connected bridgeless interval graph G. Further, for every 2-connected proper interval graph G, we show \(OD(G) \leq \lceil \frac{5}{4} diam(G) \rceil + 1\) if diam(G) ≤ 3 and \(OD(G) \leq \lceil \frac{5}{4} diam(G) \rceil\), otherwise. All the bounds are sharp and improve earlier estimations obtained by Fomin et al.

Keywords

Diameter orientation oriented diameter interval graph proper interval graph 

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Jing Huang
    • 1
  • Dong Ye
    • 2
  1. 1.Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, B.C., Canada, V8W 3P4 
  2. 2.School of mathematics and Statistics, Lanzhou University, Lanzhou, Gansu, 730000People’s Republic of China

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