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Triangles in Regular Graphs with Density Below One Half

  • ALLAN SIU LUN LO (a1)
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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[1]Ahlswede, R. and Katona, G. O. H. (1978) Graphs with maximal number of adjacent pairs of edges. Acta Math. Acad. Sci. Hungar. 32 97120.
[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 205218.
[3]Das, K. (2004) Maximizing the sum of the squares of the degrees of a graph. Discrete Math. 285 5766.
[4]de Caen, D. (1998) An upper bound on the sum of squares of degrees in a graph. Discrete Math. 185 245248.
[5]Lo, A. Cliques in graphs with bounded minimum degree. In preparation.
[6]Nikiforov, V. (2007) The sum of the squares of degrees: Sharp asymptotics. Discrete Math. 307 31873193.
[7]Olpp, D. (1996) A conjecture of Goodman and the multiplicities of graphs. Austral. J. Combin. 14 267282.
[8]Székely, L. A., Clark, L. H. and Entriger, R. C. (1992) An inequality for degree sequences. Discrete Math. 103 293300.
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Combinatorics, Probability and Computing
  • ISSN: 0963-5483
  • EISSN: 1469-2163
  • URL: /core/journals/combinatorics-probability-and-computing
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