5 papers · 1 filter
Lollipops, dense cycles and chords
ZdenÄk DvoÅák, 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 $…
Small hitting sets for longest paths and cycles
Sergey Norin, Raphael Steiner, Stephan Thomassé +1
Motivated by an old question of Gallai (1966) on the intersection of longest paths in a graph and the well-known conjectures of Lovász (1969) and Thomassen (1978) on the maximum l…
Two-block paths in oriented graphs of large semidegree
Irena Penev, S Taruni, Stéphan Thomassé +2
We study the existence of oriented paths with two blocks in oriented graphs under semidegree conditions. A block of an oriented path is a maximal directed subpath. Given positive i…
A structural description of Zykov and Blanche Descartes graphs
Malory Marin, Stéphan Thomassé, Nicolas Trotignon +1
In 1949, Zykov proposed the first explicit construction of triangle-free graphs with arbitrarily large chromatic number. We define a Zykov graph as any induced subgraph of a graph…
On the complexity of Client-Waiter and Waiter-Client games
Valentin Gledel, Nacim Oijid, Sébastien Tavenas +1
Positional games were introduced by Hales and Jewett in 1963, and their study became more popular after Erdos and Selfridge's first result on their connection to Ramsey theory and…