## Surveys in Combinatorics 2005This volume contains survey articles based on the invited lectures given at the Twentieth British Combinatorial Conference, organized jointly by the University of Durham and the Open University. It was held in July 2005 at the University of Durham. This biennial conference is a well-established international event, with speakers from all over the world. By its nature this volume provides an up-to-date overview of current research activity in several areas of combinatorics, ranging from combinatorial number theory to geometry. The authors are some of the world's foremost researchers in their fields. |

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### Contents

The subgroup structure of finite classical groups in terms | 29 |

Constructing combinatorial objects via cliques | 57 |

Flocks of circle planes | 83 |

An isoperimetric method for the small sumset problem | 119 |

The structure of clawfree graphs | 153 |

The multivariate link polynomial alias Potts model | 173 |

The sparse regularity lemma and its applications | 227 |

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1eds 3-colourable 9raph 9roups of order abelian group adjacent algebraic arithmetic progression atoms automorphism bipartite graph cardinality Cayley graphs chromatic polynomial chromatic roots classical groups claw-free graphs clique algorithm combinatorial complete graph Conjecture 3.11 connected consider construction contains corresponding cosets critical pairs define denote density Discrete Math e-regular ed9es elements Erdos exact cover example finite field flocks Geom geometric GF(q graph G graph theory group G half-plane property implies inequality integer inversive plane isomorphic judicious partitioning least Let G linear lower bound matrix matroids Max Cut maximal subgroups multivariate Tutte polynomial nonempty number of edges number theory obtained orthogonal ovoid P.R.J. Ostergard pairwise partition classes Penttila PG(n points Potts model prime proof Proposition prove q odd quadric quasi-line graphs random result Ruzsa satisfies spanning forests Spn(q stabilizer subgraph subset subspace Szemeredi's regularity lemma triangles Tutte polynomial vector vertex set vertices weight Y.O. Hamidoune

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