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    Guillot, Dominique Khare, Apoorva and Rajaratnam, Bala 2016. Critical exponents of graphs. Journal of Combinatorial Theory, Series A, Vol. 139, p. 30.


    Hell, Pavol and Hernández-Cruz, César 2016. Strict chordal and strict split digraphs. Discrete Applied Mathematics,


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    Fang, J. and Morse, A. S. 2008. 2008 47th IEEE Conference on Decision and Control. p. 1091.

    Erdős, Paul Ordman, Edward T. and Zalcstein, Yechezkel 1993. Clique Partitions of Chordal Graphs. Combinatorics, Probability and Computing, Vol. 2, Issue. 04, p. 409.


    McMorris, F. R. and Scheinerman, Edward R. 1991. Connectivity threshold for random chordal graphs. Graphs and Combinatorics, Vol. 7, Issue. 2, p. 177.


    Tyshkevich, R. I. Chernyak, A. A. and Chernyak, Zh. A. 1988. Graphs and degree sequences. I. Cybernetics, Vol. 23, Issue. 6, p. 734.


    Wormald, Nicholas C. 1987. Generating Random Unlabelled Graphs. SIAM Journal on Computing, Vol. 16, Issue. 4, p. 717.


    Wormald, Nicholas C. 1985. Counting labelled chordal graphs. Graphs and Combinatorics, Vol. 1, Issue. 1, p. 193.


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  • Currently known as: Journal of the Australian Mathematical Society Title history
    Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics, Volume 38, Issue 2
  • April 1985, pp. 214-221

Almost all chordal graphs split

  • E. A. Bender (a1), L. B. Richmond (a2) and N. C. Wormald (a3)
  • DOI: http://dx.doi.org/10.1017/S1446788700023077
  • Published online: 01 April 2009
Abstract
Abstract

A chordal graph is a graph in which every cycle of length at least 4 has a chord. If G is a random n-vertex labelled chordal graph, the size of the larget clique in about n/2 and deletion of this clique almost surely leaves only isolated vertices. This gives the asymptotic number of chordal graphs and information about a variety of things such as the size of the largest clique and connectivity.

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

[1]P. Buneman , ‘A characterisation of rigid circuit graphs’, Discrete Math. 9 (1974), 205212.

[2]G. A. Dirac , ‘On rigid circuit graphs’, Abh. Math. Sem. Univ. Hamburg 25 (1961), 7176.

[4]F. Gavril , ‘The intersection graphs of subtrees in trees are exactly the chordal graphs’, J. Combin. Theory Ser. B 16 (1974), 4756.

[5]D. J. Rose , ‘Triangulated graphs and the elimination process’, J. Math. Anal. Appl. 32 (1970), 597609.

[6]D. J. Rose , R. E. Tarjan and G. S. Lueker , ‘Algorithmic aspects of vertex elimination on graphs’, SIAM J. Comput. 5 (1976), 266283.

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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