An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyárfás made the conjecture that for all t there exists n such that every graph with no Kt subgraph and no odd hole is n-colourable. We prove this conjecture.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Induced subgraphs
- Odd holes