8 papers · 1 filter
A minimum-degree threshold for colour-biased Hamilton cycles in hypergraphs
Natalie Behague, Felix Christian Clemen, Joseph Hyde +1
We determine the asymptotically best possible minimum vertex degree condition forcing a two-coloured -graph to contain a colour-biased tight Hamilton cycle. This confirms a conj…
A note on inverting the dijoin of oriented graphs
Natalie Behague, Tom Johnston, Natasha Morrison +1
For an oriented graph and a set , the inversion of in is the graph obtained from by reversing the orientation of each edge that has both endpoints…
Universality for transversal powers of Hamilton cycles
Emily Heath, Joseph Hyde, Natasha Morrison +1
Let and let be a collection of graphs on a common vertex set of cardinality . We show that if each graph in has minimum degree…
Thresholds for constrained Ramsey and anti-Ramsey problems
Natalie Behague, Robert Hancock, Joseph Hyde +2
Let and be graphs. A graph has the constrained Ramsey property for if every edge-colouring of contains either a monochromatic copy of or a rai…
Using polynomials to find lower bounds for -bond bootstrap percolation
Natasha Morrison, Shannon Ogden
The -bond bootstrap percolation process on a graph begins with a set of infected edges of (all other edges are healthy). At each step, a healthy edge becomes infecte…
On multicolor Turán numbers
József Balogh, Anita Liebenau, LetÃcia Mattos +1
We address a problem which is a generalization of Turán-type problems recently introduced by Imolay, Karl, Nagy and Váli. Let be a fixed graph and let be the union of …