Triangles in random graphs

We show the number of triangles of G n , 1 / 2 is almost uniformly distributed among residue classes modulo q, where q is a prime number bounded by Θ ( log n ) . This implies a consequence of a conjecture of Bollobás, Pebody and Riordan (that almost every random graph G n , 1 / 2 is uniquely determi...

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Bibliographic Details
Published inDiscrete mathematics Vol. 289; no. 1; pp. 181 - 185
Main Authors Loebl, Martin, Matoušek, Jiří, Pangrác, Ondřej
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier B.V 28.12.2004
Elsevier
Subjects
Algebra
Combinatorics
Combinatorics. Ordered structures
Exact sciences and technology
Graph theory
Mathematics
Number of triangles
Number theory
Random graph
Sciences and techniques of general use
Tutte polynomial
Number of triangles
Tutte polynomial
Random graph
Discrete mathematics
Prime number
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Summary:We show the number of triangles of G n , 1 / 2 is almost uniformly distributed among residue classes modulo q, where q is a prime number bounded by Θ ( log n ) . This implies a consequence of a conjecture of Bollobás, Pebody and Riordan (that almost every random graph G n , 1 / 2 is uniquely determined by its Tutte polynomial): almost every pair of independently chosen random graphs G n , 1 / 2 has different Tutte polynomials.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2004.08.008