A tamed family of trianglefree graphs with unbounded chromatic number
A tamed family of trianglefree graphs with unbounded chromatic number

Nicolas Trotignon, CNRS and ENS de Lyon
Fine Hall 224
We construct a hereditary class of trianglefree graphs with unbounded chromatic number, in which every graph on at least three vertices either contains a pair of nonadjacent twins or has an edgeless vertex cutset of size at most two. This answers in the negative a question of Chudnovsky, Penev, Scott and the speaker. These graphs are structurally simple in several ways, in particular regarding their twinwidth. Also, we show how to obtain such graphs with arbitrarily large odd girth. This is joint work with Édouard Bonnet, Romain Bourneuf, Julien Duron, Colin Geniet and Stéphan Thomassé.