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Triangles in Regular Graphs with Density Below One Half

Published online by Cambridge University Press:  01 May 2009

Department of Pure Mathematics and Mathematical Statistics, University of Cambridge, Cambridge CB3 0WB, UK (e-mail:


Let k3reg(n, d) be the minimum number of triangles in d-regular graphs with n vertices. We find the exact value of k3reg(n, d) for d between and n/2. In addition, we identify the structure of the extremal graphs.

Copyright © Cambridge University Press 2009

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