4 papers
On the structure of (, , )-free graphs
Chính T. Hoàng, Ramin Javadi, Nicolas Trotignon
Determining the complexity of colouring ()-free graph is a long open problem. Recently Penev showed that there is a polynomial-time algorithm to colour a ($4K_1, C_4, C_…
Pathographs and some (un)decidability results
Daniel Carter, Nicolas Trotignon
We introduce pathographs as a framework to study graph classes defined by forbidden structures, including forbidding induced subgraphs, minors, etc. Pathographs approximately gener…
Every Graph is Essential to Large Treewidth
Bogdan Alecu, Édouard Bonnet, Pedro Bureo Villafana +1
We show that for every graph , there is a hereditary weakly sparse graph class of unbounded treewidth such that the -free (i.e., excluding as an induced su…
Lollipops, dense cycles and chords
Zdeněk Dvořák, Beatriz Martins, Stéphan Thomassé +1
In 1980, Gupta, Kahn and Robertson proved that every graph with minimum degree at least contains a cycle containing at least vertices each having at least $…