3 papers
math.CO2026
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…
math.CO2026
Spanning tight components in 4-uniform hypergraphs
Francesco Di Braccio, Brian Hearn, Joanna Lada +2
We prove that every -vertex 4-uniform hypergraph with minimum codegree at least has a spanning tight component. This is tight, and it settles the 4-uniform…
math.CO2025
Leaf-to-leaf paths and cycles in degree-critical graphs
Francesco Di Braccio, Kyriakos Katsamaktsis, Jie Ma +2
An -vertex graph is degree 3-critical if it has edges and no proper induced subgraph with minimum degree at least 3. In 1988, Erdős, Faudree, Gyárfás, and Schelp asked…