Rutger Campbell

activity

20152023

most citedProduct structure of graph classes with bounded treewidth

5 citations · 7 across the 6 of their papers we have counts for

collaborators

7 papers

math.CO2023

Decompositions into two linear forests of bounded lengths

Rutger Campbell, Florian Hörsch, Benjamin Moore

For some $k \in Z_{\geq 0} \cup \infty$ , we call a linear forest $k$ -bounded if each of its components has at most $k$ edges. We will say a $(k, ℓ)$ -bounded linear forest…

math.CO2022

Graphs of Linear Growth have Bounded Treewidth

Rutger Campbell, Marc Distel, J. Pascal Gollin +5

A graph class $G$ has linear growth if, for each graph $G \in G$ and every positive integer $r$ , every subgraph of $G$ with radius at most $r$ contains $O (r)$ v…

math.CO2022★ 5 cited

Product structure of graph classes with bounded treewidth

Rutger Campbell, Katie Clinch, Marc Distel +8

We show that many graphs with bounded treewidth can be described as subgraphs of the strong product of a graph with smaller treewidth and a bounded-size complete graph. To this end…

math.CO2019

On Density-Critical Matroids

Rutger Campbell, Kevin Grace, James Oxley +1

For a matroid $M$ having $m$ rank-one flats, the density $d (M)$ is $\frac{m}{r ( M )}$ unless $m = 0$ , in which case $d (M) = 0$ . A matroid is density-critical if all of its proper min…

math.CO2018

On the complex-representable excluded minors for real-representability

Rutger Campbell, Jim Geelen

We show that each real-representable matroid is a minor of a complex-representable excluded minor for real-representability. More generally, for an infinite field $F_{1}$ an…

math.CO2016★ 2 cited

Dense PG(n-1,2)-free binary matroids

Rutger Campbell

For each integer $n \geq 2$ , we prove that, if $M$ is a simple rank- $r$ $P G (n - 1, 2)$ -free binary matroid with $∣ M ∣ > (1 - \frac{3}{2 ^{n}}) 2^{r}$ , then there is a triangle-free co…

math.CO2015

On the structure of dense triangle-free binary matroids

Rutger Campbell, Jim Geelen, Peter Nelson

We prove, by means of an exact structural description, that every simple triangle-free binary matroid $M$ with $∣ M ∣ > \frac{33}{128} 2^{r (M)}$ has critical number at most $2$ .