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Combinatorica

, Volume 5, Issue 4, pp 295–300 | Cite as

On the existence of two non-neighboring subgraphs in a graph

  • M. El-Zahar
  • P. Erdős
Article

Abstract

Does there exist a functionf(r, n) such that each graphG with Z (G)≧f(r, n) contains either a complete subgraph of orderr or else two non-neighboringn-chromatic subgraphs? It is known thatf(r, 2) exists and we establish the existence off(r, 3). We also give some interesting results about graphs which do not contain two independent edges.

AMS subject classification (1980)

05 C 15 

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References

  1. [1]
    J. Mycielski, Sur le coloriage des graphes,Colloq. Math.3 (1955), 161–162.zbMATHMathSciNetGoogle Scholar
  2. [2]
    S. Wagon, A bound on the chromatic number of graphs without certain induced subgraphs,J. Combinatorial Theory Ser. B29 (1980), 345–346.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    P. Erdős, On circuits and subgraphs of chromatic graphs,Mathematika9 (1962), 170–175.MathSciNetCrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 1985

Authors and Affiliations

  • M. El-Zahar
    • 1
  • P. Erdős
    • 2
  1. 1.Department of MathematicsUniversity of CalgaryCanada
  2. 2.Mathematical Institute of the Hungarian Academy of SciencesHungary

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