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On the Maximum Number of Triangles in Wheel-Free Graphs

Published online by Cambridge University Press:  12 September 2008

Zoltán Füredi ,
Michel X. Goemans  and
Daniel J. Kleitman
Zoltán Füredi
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
Michel X. Goemans
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
Daniel J. Kleitman
Affiliation:
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

Gallai [1] raised the question of determining t(n), the maximum number of triangles in graphs of n vertices with acyclic neighborhoods. Here we disprove his conjecture (t(n) ~ n2/8) by exhibiting graphs having n2/7.5 triangles. We improve the upper bound [11] of (n2 − n)/6 to t(n) ≤; n2/7.02 + O(n). For regular graphs, we further decrease this bound to n2/7.75 + O(n).

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 3 , Issue 1 , March 1994 , pp. 63 - 75
Copyright
Copyright © Cambridge University Press 1994

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