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Triangles in Regular Graphs with Density Below One Half
Published online by Cambridge University Press: 01 May 2009
Abstract
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.
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References
[1]Ahlswede, R. and Katona, G. O. H. (1978) Graphs with maximal number of adjacent pairs of edges. Acta Math. Acad. Sci. Hungar. 32 97–120.Google Scholar
[2]Andrásfai, B., Erdős, P. and Sós, V. T. (1974) On the connection between chromatic number, maximal clique and minimal degree of a graph. Discrete Math. 8 205–218.Google Scholar
[3]Das, K. (2004) Maximizing the sum of the squares of the degrees of a graph. Discrete Math. 285 57–66.CrossRefGoogle Scholar
[4]de Caen, D. (1998) An upper bound on the sum of squares of degrees in a graph. Discrete Math. 185 245–248.CrossRefGoogle Scholar
[6]Nikiforov, V. (2007) The sum of the squares of degrees: Sharp asymptotics. Discrete Math. 307 3187–3193.CrossRefGoogle Scholar
[7]Olpp, D. (1996) A conjecture of Goodman and the multiplicities of graphs. Austral. J. Combin. 14 267–282.Google Scholar
[8]Székely, L. A., Clark, L. H. and Entriger, R. C. (1992) An inequality for degree sequences. Discrete Math. 103 293–300.CrossRefGoogle Scholar
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