## Faculty Publications & Research

#### Document Type

Article

#### Publication Date

2009

#### Disciplines

Discrete Mathematics and Combinatorics | Mathematics

#### Abstract

Erdős and Lovász conjectured in 1968 that for every graph *G* with *χ(G)* > *ω*(*G*) and any two integers *s*,* t ≥ *2 with *s* + *t* = *χ*(*G*) + 1, there is a partition (*S,T*) of the vertex set *V*(*G*) such that *χ*(*G*[*S*]) ≥ *s *and *χ*(*G*[*T*]) ≥ *t* . Except for a few cases, this conjecture is still unsolved. In this note we prove the conjecture for quasi-line graphs and for graphs with independence number 2.

#### Recommended Citation

Balogh, J., Kostochka, A.V., Prince, N., & Stiebitz, M. (2009). The Erdős-Lovász Tihany conjecture for quasi-line graphs. *Discrete Mathematics,* 309(12), 3985-3991.

## Comments

At the time of publication, Noah Prince was affiliated with the University of Illinois at Urbana-Champaign.