# Gyarfas, Andras

## Graphs with a forbidden induced tree are chi-bounded ★★★

Author(s): Gyarfas

Say that a family of graphs is -bounded if there exists a function so that every satisfies .

Conjecture   For every fixed tree , the family of graphs with no induced subgraph isomorphic to is -bounded.

Keywords: chi-bounded; coloring; excluded subgraph; tree

## Bounding the chromatic number of graphs with no odd hole ★★★

Author(s): Gyarfas

Conjecture   There exists a fixed function so that for every graph with no odd hole.