### Abstract

We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph H, then these graphs have a structure that is asymptotically the same as the structure of H. Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of

Original language | English |
---|---|

Pages (from-to) | 146-163 |

Number of pages | 18 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 98 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2008 |

### Fingerprint

### Keywords

- Convergent graph sequence
- Graph algebra
- Homomorphism
- Quasirandom graph

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Theoretical Computer Science

### Cite this

*Journal of Combinatorial Theory. Series B*,

*98*(1), 146-163. https://doi.org/10.1016/j.jctb.2007.06.005

**Generalized quasirandom graphs.** / Lovász, L.; Sós, Vera T.

Research output: Contribution to journal › Article

*Journal of Combinatorial Theory. Series B*, vol. 98, no. 1, pp. 146-163. https://doi.org/10.1016/j.jctb.2007.06.005

}

TY - JOUR

T1 - Generalized quasirandom graphs

AU - Lovász, L.

AU - Sós, Vera T.

PY - 2008/1

Y1 - 2008/1

N2 - We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph H, then these graphs have a structure that is asymptotically the same as the structure of H. Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of

AB - We prove that if a sequence of graphs has (asymptotically) the same distribution of small subgraphs as a generalized random graph modeled on a fixed weighted graph H, then these graphs have a structure that is asymptotically the same as the structure of H. Furthermore, it suffices to require this for a finite number of subgraphs, whose number and size is bounded by a function of

KW - Convergent graph sequence

KW - Graph algebra

KW - Homomorphism

KW - Quasirandom graph

UR - http://www.scopus.com/inward/record.url?scp=36049039289&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=36049039289&partnerID=8YFLogxK

U2 - 10.1016/j.jctb.2007.06.005

DO - 10.1016/j.jctb.2007.06.005

M3 - Article

AN - SCOPUS:36049039289

VL - 98

SP - 146

EP - 163

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

SN - 0095-8956

IS - 1

ER -