30 citations · 114 across the 29 of their papers we have counts for
37 papers · 1 filter
Local Resilience for Containment of Bounded Degree Spanning Subgraphs
Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa +1
We prove that for all and , there exists a constant such that for , asymptotically almost surely, every spanning subgraph …
A generalised transference principle
Peter Allen, Julia Böttcher, Joanna Lada +1
The last two decades have witnessed a growing trend towards proving sparse random analogues of combinatorial theorems. One unified approach to proving such theorems, formalised by…
Breaking the Bollobás-Eldridge-Catlin Barrier for Bipartite Graphs
Peter Allen, Julia Böttcher, Jozef Skokan +1
The celebrated Bollobás-Eldridge-Catlin packing conjecture states that every -vertex graph with minimum degree at least contains every -vert…
Universality for graphs of bounded degeneracy
Peter Allen, Julia Böttcher, Anita Liebenau
Given a family of graphs, a graph is called -universal if contains every graph of as a subgraph. Following the extensive research o…
A robust Corrádi--Hajnal Theorem
Peter Allen, Julia Böttcher, Jan Corsten +5
For a graph and , we denote by the random sparsification of obtained by keeping each edge of independently, with probability . We show that there ex…
The square of a Hamilton cycle in randomly perturbed graphs
Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1
We investigate the appearance of the square of a Hamilton cycle in the model of randomly perturbed graphs, which is, for a given , the union of any -vertex graph wit…