6 papers
On -factors of Hamiltonian graphs
Alberto Espuny DÃaz, António Girão, Bertille Granet +1
Let . We show that, for a sufficiently small , any sufficiently large -vertex Hamiltonian graph of minimum degree at least contains a…
Sharp Fuss-Catalan thresholds in graph bootstrap percolation
Zsolt Bartha, Brett Kolesnik, Gal Kronenberg +1
We study graph bootstrap percolation on the ErdÅs-Rényi random graph . For all , we locate the sharp -percolation threshold $p_c \sim (γn)^{-1/…
Decomposing cubic graphs into isomorphic linear forests
Gal Kronenberg, Shoham Letzter, Alexey Pokrovskiy +1
A common problem in graph colouring seeks to decompose the edge set of a given graph into few similar and simple subgraphs, under certain divisibility conditions. In 1987 Wormald c…
Shotgun assembly of random graphs
Tom Johnston, Gal Kronenberg, Alexander Roberts +1
In the graph shotgun assembly problem, we are given the balls of radius around each vertex of a graph and asked to reconstruct the graph. We study the shotgun assembly of the E…
A note on improved bounds for hypergraph rainbow matching problems
Candida Bowtell, Andrea Freschi, Gal Kronenberg +1
A natural question, inspired by the famous Ryser-Brualdi-Stein Conjecture, is to determine the largest positive integer such that every collection of matchings, each o…
A multidimensional Ramsey Theorem
António Girão, Gal Kronenberg, Alex Scott
Ramsey theory is a central and active branch of combinatorics. Although Ramsey numbers for graphs have been extensively investigated since Ramsey's work in the 1930s, there is stil…