Peter Allen

activity

20102022

most citedRegularity inheritance in hypergraphs

3 citations · 7 across the 8 of their papers we have counts for

collaborators

Showing math.COShow all

11 papers · 1 filter

math.CO2022

Partition universality for graphs of bounded degeneracy and degree

Peter Allen, Julia Böttcher

We prove asymptotically optimal bounds on the number of edges a graph $G$ must have in order that any $r$ -colouring of $E (G)$ has a colour class which contains every $D$ -degenerate…

math.CO2021

Resilience for tight Hamiltonicity

Peter Allen, Olaf Parczyk, Vincent Pfenninger

We prove that random hypergraphs are asymptotically almost surely resiliently Hamiltonian. Specifically, for any $γ > 0$ and $k \geq 3$ , we show that asymptotically almost surely, every…

math.CO2019

A spanning bandwidth theorem in random graphs

Peter Allen, Julia Böttcher, Julia Ehrenmüller +2

The bandwidth theorem [Mathematische Annalen, 343(1):175--205, 2009] states that any $n$ -vertex graph $G$ with minimum degree $(\frac{k - 1}{k} + o (1)) n$ contains all $n$ -vertex $k$ -co…

math.CO2019★ 1 cited

Perfectly packing graphs with bounded degeneracy and many leaves

Peter Allen, Julia Böttcher, Dennis Clemens +1

We prove that one can perfectly pack degenerate graphs into complete or dense $n$ -vertex quasirandom graphs, provided that all the degenerate graphs have maximum degree $o(\frac{n}…

math.CO2019★ 3 cited

Regularity inheritance in hypergraphs

Peter Allen, Ewan Davies, Jozef Skokan

We give a new approach to handling hypergraph regularity. This approach allows for vertex-by-vertex embedding into regular partitions of hypergraphs, and generalises to regular par…

math.CO2017★ 3 cited

Making spanning graphs

Peter Allen, Julia Böttcher, Yoshiharu Kohayakawa +2

We prove that for each $D \geq 2$ there exists $c > 0$ such that whenever $b \leq c (\frac{n}{l o g n})^{1/ D}$ , in the $(1 : b)$ Maker-Breaker game played on $E (K_{n})$ , Maker has a s…