Browsing Combinatorics and Optimization by Author "Chudnovsky, Maria"

Now showing items 21-23 of 23

Towards Erdős-Hajnal for Graphs with No 5-Hole

Chudnovsky, Maria; Fox, Jacob; Scott, Alex; Seymour, Paul; Spirkl, Sophie (Springer Nature, 2019-11-01)

The Erdős-Hajnal conjecture says that for every graph H there exists c > 0 such that max(α(G), w(G)) ≥ nc for every H-free graph G with n vertices, and this is still open when H = C5. Until now the best bound known on ...
Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable

Chudnovsky, Maria; Liu, Chun-Hung; Schaudt, Oliver; Spirkl, Sophie; Trotignon, Nicolas; Vušković, Kristina (Wiley, 2019-10)

We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vušković.
Triangle-free graphs with no six-vertex induced path

Chudnovsky, Maria; Seymour, Paul; Spirkl, Sophie; Zhong, Mingxian (Elsevier, 2018-08)

The graphs with no five-vertex induced path are still not understood. But in the triangle-free case, we can do this and one better; we give an explicit construction for all triangle-free graphs with no six-vertex induced ...