4 papers · 1 filter
Towards Pósa's Conjecture for -graphs
Debmalya Bandyopadhyay, Allan Lo, Richard Mycroft
We prove that every -graph on vertices with minimum codegree contains the square of a tight Hamilton cycle. This strengthens a theorem of Beden…
Compatible Hamilton cycles in graphs with large minimum degree
Natalie Behague, Francesco Di Braccio, Bertille Granet +1
The renowned theorem of Dirac states that if is a graph with minimum degree at least then has a Hamilton cycle. A natural generalisation asks what properties of an ed…
Powers of Hamilton cycles in oriented and directed graphs
Louis DeBiasio, Jie Han, Allan Lo +3
The Pósa--Seymour conjecture determines the minimum degree threshold for forcing the th power of a Hamilton cycle in a graph. After numerous partial results, Komlós, Sárközy and…
Spanning trees with few branch vertices
Louis DeBiasio, Allan Lo
A branch vertex in a tree is a vertex of degree at least three. We prove that, for all , every connected graph on vertices with minimum degree at least $(\frac{1}{s+3}…