Graphs and Combinatorics

, Volume 8, Issue 2, pp 165–197 | Cite as

Large regular graphs with no induced 2K2

  • Madeleine Paoli
  • G. W. Peck
  • W. T. TrotterJr.
  • Douglas B. West
Original Papers

Abstract

Letr be a positive integer. Considerr-regular graphs in which no induced subgraph on four vertices is an independent pair of edges. The numberv of vertices in such a graph does not exceed 5r/2; this proves a conjecture of Bermond. More generally, it is conjectured that ifv>2r, then the ratiov/r must be a rational number of the form 2+1/(2k). This is proved forv/r≥21/10. The extremal graphs and many other classes of these graphs are described and characterized.

Keywords

Positive Integer Rational Number Regular Graph Extremal Graph Independent Pair 

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References

  1. 1.
    Bermond, J.-C., Bond, J., Paoli, M. and Peyrat, C.: Graphs and interconnection networks: Diameter and vulnerability.Surveys in Combinatorics, Lond. Math. Soc. Lect. Notes (1983) 1–29Google Scholar
  2. 2.
    Bermond, J.-C., Bond, J. and Peyrat, C.: Bus interconnection networks with each station on two buses.Proc. Coll. Int. Algor. et Arch. Paralleles (Marseilles) (North-Holland 1986), 155–167Google Scholar
  3. 3.
    Chung, F.R.K., Gyárfás, A., Tuza, Z. and Trotter, W.T.: The maximum number of edges in a 2K 2-free graph,Discrete Math. Discrete Math. 81 (1990), 129–135Google Scholar
  4. 4.
    Chung, M.-S., and West, D.B.: LargeP 4-free graphs with bounded degree (submitted)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Madeleine Paoli
    • 1
  • G. W. Peck
    • 2
  • W. T. TrotterJr.
    • 3
  • Douglas B. West
    • 4
  1. 1.University of South CarolinaColumbiaUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA
  3. 3.BellcoreMorristowUSA
  4. 4.University of IllinoisUrbanaUSA

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