421 citations
Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.
- University College LondonGB63 papers
- Systemic Risk CentreGB48 papers
- University of OxfordGB20 papers
- University of WarwickGB18 papers
- King's College LondonGB16 papers
- London Mathematical LaboratoryGB12 papers
- University of Illinois Urbana-ChampaignUS12 papers
- Centre National de la Recherche ScientifiqueFR11 papers
- Queen Mary University of LondonGB11 papers
- The Open UniversityGB11 papers
- City, University of LondonGB10 papers
- ETH ZurichCH10 papers
10 papers · 2 filters
Chromatic Numbers of Exact Distance Graphs
Jan van den Heuvel, H. A. Kierstead, Daniel A. Quiroz
For any graph and positive integer , the exact distance- graph is the graph with vertex set , which has an edge between vertices and i…
Blow-up lemmas for sparse graphs
Peter Allen, Julia Böttcher, Hiep Hàn +2
The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. Thi…
Extremes of the internal energy of the Potts model on cubic graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove tight upper and lower bounds on the internal energy per particle (expected number of monochromatic edges per vertex) in the anti-ferromagnetic Potts model on cubic graphs…
Almost all trees are almost graceful
Anna Adamaszek, Peter Allen, Codrut Grosu +1
The Graceful Tree Conjecture of Rosa from 1967 asserts that the vertices of each tree T of order n can be injectively labelled by using the numbers {1,2,...,n} in such a way that t…
On sets defining few ordinary circles
Aaron Lin, Mehdi Makhul, Hossein Nassajian Mojarrad +3
An ordinary circle of a set of points in the plane is defined as a circle that contains exactly three points of . We show that if is not contained in a line or a cir…
Regularity inheritance in pseudorandom graphs
Peter Allen, Julia Böttcher, Jozef Skokan +1
Advancing the sparse regularity method, we prove one-sided and two-sided regularity inheritance lemmas for subgraphs of bijumbled graphs, improving on results of Conlon, Fox and Zh…
On the average size of independent sets in triangle-free graphs
Ewan Davies, Matthew Jenssen, Will Perkins +1
We prove an asymptotically tight lower bound on the average size of independent sets in a triangle-free graph on vertices with maximum degree , showing that an independent s…
Multicolour Ramsey numbers of paths and even cycles
Ewan Davies, Matthew Jenssen, Barnaby Roberts
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that . The upper bound was…
An asymptotic multipartite Kühn-Osthus theorem
Ryan R. Martin, Richard Mycroft, Jozef Skokan
In this paper we prove an asymptotic multipartite version of a well-known theorem of Kühn and Osthus by establishing, for any graph with chromatic number , the asymptotic mu…
On the Generalised Colouring Numbers of Graphs that Exclude a Fixed Minor
Jan van den Heuvel, Patrice Ossona de Mendez, Daniel Quiroz +2
The generalised colouring numbers and were introduced by Kierstead and Yang as a generalisation of the usual colouring number, and have sin…