The coloring and maximum independent set problems on planar perfect graphs
Journal of the ACM (JACM)
Discrete Applied Mathematics - Combinatorics and complexity
On the NP-completeness of the k-colorability problem for triangle-free graphs
Discrete Mathematics
Optimizing Bull-Free Perfect Graphs
SIAM Journal on Discrete Mathematics
Combinatorica
Coloring Bull-Free Perfectly Contractile Graphs
SIAM Journal on Discrete Mathematics
Journal of Graph Theory
The Erdős--Hajnal conjecture for bull-free graphs
Journal of Combinatorial Theory Series B
Claw-free graphs. V. Global structure
Journal of Combinatorial Theory Series B
Claw-free graphs VI. Colouring
Journal of Combinatorial Theory Series B
The structure of bull-free graphs II and III-A summary
Journal of Combinatorial Theory Series B
The structure of bull-free graphs II and III-A summary
Journal of Combinatorial Theory Series B
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The bull is the graph consisting of a triangle and two disjoint pendant edges. A graph is called bull-free if no induced subgraph of it is a bull. This is the first paper in a series of three. The goal of the series is to explicitly describe the structure of all bull-free graphs. In this paper we study the structure of bull-free graphs that contain as induced subgraphs three-edge-paths P and Q, and vertices c@?V(P) and a@?V(Q), such that c is adjacent to every vertex of V(P) and a has no neighbor in V(Q). One of the theorems in this paper, namely 1.2, is used in Chudnovsky and Safra (2008) [9] in order to prove that every bull-free graph on n vertices contains either a clique or a stable set of size n^1^4, thus settling the Erdos-Hajnal conjecture (Erdos and Hajnal, 1989) [17] for the bull.