Polynomial bounds for chromatic number VIII. Excluding a path and a complete multipartite graph
Tung Thanh Nguyen, Alex Scott, Paul D. Seymour · Journal of Graph Theory · 2024
Abstract We prove that for every path , and every integer , there is a polynomial such that every graph with chromatic number greater than either contains as an induced subgraph, or contains as a subgraph the complete ‐partite graph with parts of cardinality . For and general this is a classical theorem of Gyárfás, and for and general this is a theorem of Bonamy et al.