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Almost all chordal graphs split

  • E. A. Bender (a1), L. B. Richmond (a2) and N. C. Wormald (a3)
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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