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


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.


Positive Integer Rational Number Regular Graph Extremal Graph Independent Pair 
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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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