### Abstract

The bull is a graph consisting of a triangle and two pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. This is a summary of the last two papers [2,3] in a series [1-3] (Chudnovsky, 2012). The goal of the series is to give a complete description of all bull-free graphs. We call a bull-free graph elementary if it does not contain an induced three-edge-path P such that some vertex c∉ V(P) is complete to V(P), and some vertex a∉ V(P) is anticomplete to V(P). Here we prove that every elementary graph either belongs to one of a few basic classes, or admits a certain decomposition, and then uses this result together with the results of [1] (this issue) to give an explicit description of the structure of all bull-free graphs.

Original language | English (US) |
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Pages (from-to) | 252-282 |

Number of pages | 31 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 102 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

### Keywords

- Bull-free graphs
- Graph structure
- Induced subgraph