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Combinatorica

, Volume 9, Issue 3, pp 245–253 | Cite as

The size of chordal, interval and threshold subgraphs

  • P. Erdös
  • A. Gyárfás
  • E. T. Ordman
  • Y. Zalcstein
Article

Abstract

Given a graphG withn vertices andm edges, how many edges must be in the largest chordal subgraph ofG? Form=n2/4+1, the answer is 3n/2−1. Form=n2/3, it is 2n−3. Form=n2/3+1, it is at least 7n/3−6 and at most 8n/3−4. Similar questions are studied, with less complete results, for threshold graphs, interval graphs, and the stars on edges, triangles, andK4's.

AMS subject classification (1980)

05 C 35 

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References

  1. [1]
    V. Chvatal andP. Hammer, Aggregation of inequalities in integer programming,Ann. Discrete Math.,1 (1977), 145–162.Google Scholar
  2. [2]
    C. S.Edwards, A lower bound for the largest number of triangles with a single edge,manuscript, (about 1977?).Google Scholar
  3. [3]
    C. S. Edwards, The largest vertex degree sum for a triangle in a graph,Bull. London Math. Soc.,9 (1977), 203–208.Google Scholar
  4. [4]
    P.Erdös and R.Laskar, A note on the size of a chordal subgraph,Proc. 1985 Southeastern International Conf. on Graphs, Combinatorics, and Computing, Utilitas Mathematica Publishing Co, 81–86.Google Scholar
  5. [5]
    P.Erdös, E.Ordman, and Y.Zalcstein, Coverings and partitions with chordal and threshold graphs,submitted for publication.Google Scholar
  6. [6]
    M. Golumbic, Algorithmic Graph Theory and Perfect Graphs,Academic Press, New York,1980.Google Scholar
  7. [7]
    P. Henderson andY. Zalcstein, A graph theoretic characterization of the PVchunk class of synchronizing primitives,SIAM J. Comp.,6 (1977), 88–108.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1989

Authors and Affiliations

  • P. Erdös
    • 1
  • A. Gyárfás
    • 2
  • E. T. Ordman
    • 3
  • Y. Zalcstein
    • 4
  1. 1.Mathematical InstituteHungarian Academy of SciencesHungary
  2. 2.Automata Theory Research GroupHungarian Academy of SciencesHungary
  3. 3.Department of Mathematical SciencesMemphis State UniversityUSA
  4. 4.Division of Computer and Computation ResearchNational Science FoundationWashington, DCUSA

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