London School of Economics and Political Science

output

19992026

most citedSparsistency and rates of convergence in large covariance matrix estimation

421 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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86 papers · 1 filter

math.CO2025

Determining a graph from its reconfiguration graph

Gaétan Berthe, Caroline Brosse, Brian Hearn +3

Given a graph $G$ and a natural number $k$ , the $k$ -recolouring graph $C_{k} (G)$ is the graph whose vertices are the $k$ -colourings of $G$ and whose edges link pairs of col…

math.CO2025

Edge isoperimetry of lattices

Cameron Strachan, Konrad Swanepoel

We present two results related to an edge-isoperimetric question for Cayley graphs on the integer lattice asked by Ben Barber and Joshua Erde [Isoperimetry of Integer Lattices, Dis…

math.CO2024

Dirac's theorem for graphs of bounded bandwidth

Alberto Espuny Díaz, Pranshu Gupta, Domenico Mergoni Cecchelli +2

We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph $K_{2, ℓ}$ . This…

math.CO2023★ 1 cited

On product Schur triples in the integers

Letícia Mattos, Domenico Mergoni Cecchelli, Olaf Parczyk

Schur's theorem states that in any $k$ -colouring of the set of integers $[n]$ there is a monochromatic solution to $a + b = c$ , provided $n$ is sufficiently large. Abbott and Wang stud…

math.CO2022

The Ramsey numbers of squares of paths and cycles

Peter Allen, Domenico Mergoni Cecchelli, Barnaby Roberts +1

The square $G^{2}$ of a graph $G$ is the graph on $V (G)$ with a pair of vertices $uv$ an edge whenever $u$ and $v$ have distance $1$ or $2$ in $G$ . Given graphs $G$ and $H$ , the Rams…

math.CO2022

Partitioning a 2-edge-coloured graph of minimum degree $2 n /3 + o (n)$ into three monochromatic cycles

Peter Allen, Julia Böttcher, Richard Lang +2

Lehel conjectured in the 1970s that every red and blue edge-coloured complete graph can be partitioned into two monochromatic cycles. This was confirmed in 2010 by Bessy and Thomas…

math.CO2022★ 1 cited

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 $α \in (0, 1)$ , the union of any $n$ -vertex graph wit…

math.CO2021★ 1 cited

On complete classes of valuated matroids

Edin Husić, Georg Loho, Ben Smith +1

We characterize a rich class of valuated matroids, called R-minor valuated matroids that includes the indicator functions of matroids, and is closed under operations such as taking…

math.CO2021★ 4 cited

Size-Ramsey numbers of powers of hypergraph trees and long subdivisions

Shoham Letzter, Alexey Pokrovskiy, Liana Yepremyan

The $s$ -colour size-Ramsey number of a hypergraph $H$ is the minimum number of edges in a hypergraph $G$ whose every $s$ -edge-colouring contains a monochromatic copy of $H$ . We sho…

math.CO2020★ 13 cited

Triangles in randomly perturbed graphs

Julia Böttcher, Olaf Parczyk, Amedeo Sgueglia +1

We study the problem of finding pairwise vertex-disjoint triangles in the randomly perturbed graph model, which is the union of any $n$ -vertex graph $G$ satisfying a given minimum…

math.CO2020★ 3 cited

Density of monochromatic infinite subgraphs II

Jan Corsten, Louis DeBiasio, Paul McKenney

In 1967, Gerencsér and Gyárfás proved a result which is considered the starting point of graph-Ramsey theory: In every 2-coloring of $K_{n}$ there is a monochromatic path on $\lceil(…

math.CO2019

Successive shortest paths in complete graphs with random edge weights

Stefanie Gerke, Balázs F. Mezei, Gregory B. Sorkin

Consider a complete graph $K_{n}$ with edge weights drawn independently from a uniform distribution $U (0, 1)$ . The weight of the shortest (minimum-weight) path $P_{1}$ between two given…

math.CO2019★ 1 cited

Bounding the tripartite-circle crossing number of complete tripartite graphs

Charles Camacho, Silvia Fernández-Merchant, Marija Jelić Milutinović +4

A tripartite-circle drawing of a tripartite graph is a drawing in the plane, where each part of a vertex partition is placed on one of three disjoint circles, and the edges do not…

math.CO2019★ 10 cited

The size-Ramsey number of powers of bounded degree trees

Sören Berger, Yoshiharu Kohayakawa, Giulia Satiko Maesaka +4

Given a positive integer $s$ , the $s$ -colour size-Ramsey number of a graph $H$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that,…

math.CO2019★ 3 cited

Uniform Orderings for Generalized Coloring Numbers

Jan van den Heuvel, H. A. Kierstead

The generalized coloring numbers col_r(G) (also denoted by scol_r(G)) and wcol_r(G) of a graph G were introduced by Kierstead and Yang as a generalization of the usual coloring num…

math.CO2019★ 2 cited

The size-Ramsey number of 3-uniform tight paths

Jie Han, Yoshiharu Kohayakawa, Shoham Letzter +2

Given a hypergraph $H$ , the size-Ramsey number $r^_{2} (H)$ is the smallest integer $m$ such that there exists a graph $G$ with $m$ edges with the property that in any colouring…

math.CO2019

The independent set problem is FPT for even-hole-free graphs

Edin Husic, Stephan Thomasse, Nicolas Trotignon

The class of even-hole-free graphs is very similar to the class of perfect graphs, and was indeed a cornerstone in the tools leading to the proof of the Strong Perfect Graph Theore…

math.CO2019

Ordinary hyperspheres and spherical curves

Aaron Lin, Konrad Swanepoel

An ordinary hypersphere of a set of points in real $d$ -space, where no $d + 1$ points lie on a $(d - 2)$ -sphere or a $(d - 2)$ -flat, is a hypersphere (including the degenerate case of a…

math.CO2019★ 4 cited

Decomposing tournaments into paths

Allan Lo, Viresh Patel, Jozef Skokan +1

We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomp…

math.CO2018★ 2 cited

The multicolour size-Ramsey number of powers of paths

Jie Han, Matthew Jenssen, Yoshiharu Kohayakawa +2

Given a positive integer $s$ , a graph $G$ is $s$ -Ramsey for a graph $H$ , denoted $G \to (H)_{s}$ , if every $s$ -colouring of the edges of $G$ contains a monochromatic copy of $…

math.CO2018

Ordinary planes, coplanar quadruples, and space quartics

Aaron Lin, Konrad Swanepoel

An ordinary plane of a finite set of points in real 3-space with no three collinear is a plane intersecting the set in exactly three points. We prove a structure theorem for sets o…

math.CO2018★ 6 cited

Matching fields and lattice points of simplices

Georg Loho, Ben Smith

We show that the Chow covectors of a linkage matching field define a bijection between certain degree vectors and lattice points, and we demonstrate how one can recover the linkage…

math.CO2018★ 12 cited

Embedding graphs in Euclidean space

Nóra Frankl, Andrey Kupavskii, Konrad J. Swanepoel

The dimension of a graph $G$ is the smallest $d$ for which its vertices can be embedded in $d$ -dimensional Euclidean space in the sense that the distances between endpoints of edge…

math.CO2017★ 1 cited

Maximizing the density of $K_{t}$ 's in graphs of bounded degree and clique number

R. Kirsch, A. J. Radcliffe

Zykov showed in 1949 that among graphs on $n$ vertices with clique number $ω (G) \leq ω$ , the Turán graph $T_{ω} (n)$ maximizes not only the number of edges but also the number of copie…

Determining a graph from its reconfiguration graph

Edge isoperimetry of lattices

Dirac's theorem for graphs of bounded bandwidth

On product Schur triples in the integers

The Ramsey numbers of squares of paths and cycles

Partitioning a 2-edge-coloured graph of minimum degree 2n/3+o(n) into three monochromatic cycles

The square of a Hamilton cycle in randomly perturbed graphs

On complete classes of valuated matroids

Size-Ramsey numbers of powers of hypergraph trees and long subdivisions

Triangles in randomly perturbed graphs

Density of monochromatic infinite subgraphs II

Successive shortest paths in complete graphs with random edge weights

Bounding the tripartite-circle crossing number of complete tripartite graphs

The size-Ramsey number of powers of bounded degree trees

Uniform Orderings for Generalized Coloring Numbers

The size-Ramsey number of 3-uniform tight paths

The independent set problem is FPT for even-hole-free graphs

Ordinary hyperspheres and spherical curves

Decomposing tournaments into paths

The multicolour size-Ramsey number of powers of paths

Ordinary planes, coplanar quadruples, and space quartics

Matching fields and lattice points of simplices

Embedding graphs in Euclidean space

Maximizing the density of Kt​'s in graphs of bounded degree and clique number

Partitioning a 2-edge-coloured graph of minimum degree $2 n /3 + o (n)$ into three monochromatic cycles

Maximizing the density of $K_{t}$ 's in graphs of bounded degree and clique number