6 papers
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…
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, ErdÅs, Faudree, Gyárfás, and Schelp ask…
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…
Monochromatic cycle partitions of -edge-coloured graphs with high minimum degree
Francesco Di Braccio, Viresh Patel
A question posed independently by Letzter and Pokrovskiy asks: how many vertex-disjoint monochromatic cycles are needed to cover the vertex set of an -edge-coloured graph, as a…
Hamilton decompositions of regular tripartite tournaments
Francesco Di Braccio, Joanna Lada, Viresh Patel +2
Kühn and Osthus conjectured in 2013 that regular tripartite tournaments are decomposable into Hamilton cycles. Somewhat surprisingly, Granet gave a simple counterexample to this c…
Leaf-to-leaf paths of many lengths
Francesco Di Braccio, Kyriakos Katsamaktsis, Alexandru Malekshahian
We prove that every tree of maximum degree with leaves contains paths between leaves of at least distinct lengths. This settles in a strong fo…