# Hoang, Chinh T.

## 2-colouring a graph without a monochromatic maximum clique ★★

**Conjecture**If is a non-empty graph containing no induced odd cycle of length at least , then there is a -vertex colouring of in which no maximum clique is monochromatic.

Keywords: maximum clique; Partitioning

## Hoàng-Reed Conjecture ★★★

**Conjecture**Every digraph in which each vertex has outdegree at least contains directed cycles such that meets in at most one vertex, .

Keywords:

## The stubborn list partition problem ★★

Author(s): Cameron; Eschen; Hoang; Sritharan

**Problem**Does there exist a polynomial time algorithm which takes as input a graph and for every vertex a subset of , and decides if there exists a partition of into so that only if and so that are independent, is a clique, and there are no edges between and ?

Keywords: list partition; polynomial algorithm