We prove that there are 24 4-critical P6-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P6, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Critical graph
- Forbidden induced paths
- Graph coloring