## PIMS - SFU Discrete Math Seminar: Sophie Spirkl

- Date: 07/21/2021
- Time: 10:30

Online

The Complexity of List-5-colouring with a Forbidden Induced Sugbraph

**Abstract:** A k-list-assignment for a graph G is a function L from V(G) to the set of subsets of {1,…,k}. The list-k-colouring problem asks, given G and a k-list-assignment L, is there a colouring f of G with f(v) in L(v) for all v in V(G)? This generalizes the k-colouring problem (where we use L(v)={1,…,k} for every vertex). For k at least 3, both k-colouring and list-k-colouring are NP-hard, which motivates studying the complexity of these problems when the input is restricted to H-free graphs (for a fixed H, excluded as an induced subgraph).

I will present an algorithm for list-5-colouring restricted to H-free graphs for all H which consist of connected components each of which is a 3-vertex path. This, together with previous results, gives a complete answer to the question, “for which H is list-5-colouring restricted to H-free graphs NP-hard? Joint work with Sepehr Hajebi and Yanjia Li.