18 citations · 62 across the 29 of their papers we have counts for
8 papers · 2 filters
An Induced -Path Theorem
Robert Hickingbotham, Gwenaël Joret
Given a graph and , a classical theorem of Gallai (1964) states that for every positive integer , the graph contains pairwise vertex-disjo…
Excluding a Forest Induced Minor
Édouard Bonnet, Benjamin Duhamel, Robert Hickingbotham
In the first paper of the Graph Minors series [JCTB '83], Robertson and Seymour proved the Forest Minor theorem: the -minor-free graphs have bounded pathwidth if and only if …
Induced Minors, Asymptotic Dimension, and Baker's Technique
Robert Hickingbotham
Asymptotic dimension is a large-scale invariant of metric spaces that was introduced by Gromov (1993). We prove that every hereditary class of bounded-degree graphs that excludes s…
Binary matroids and degree-boundedness for pivot-minors
Rutger Campbell, James Davies, Robert Hickingbotham
We prove that for every bipartite graph and positive integer , the class of -subgraph-free graphs excluding as a pivot-minor has bounded average degree. Our pro…
Coarse Balanced Separators and Tree-Decompositions
Maria Chudnovsky, Robert Hickingbotham
A classical result of Robertson and Seymour (1986) states that the treewidth of a graph is linearly tied to its separation number: the smallest integer such that, for every wei…
Induced Minors and Region Intersection Graphs
Édouard Bonnet, Robert Hickingbotham
We show that for any positive integers and , there is a -induced-minor-free graph of girth at least that is not a region intersection graph over the class o…
Quasi-isometries between graphs with variable edge lengths
James Davies, Meike Hatzel, Robert Hickingbotham
This paper investigates quasi-isometries between graphs with variable edge lengths. A quasi-isometry is a mapping between metric spaces that approximately preserves distances, allo…
Graphs that are quasi-isometric to graphs with bounded treewidth
Robert Hickingbotham
In this paper, we characterise graphs that are quasi-isometric to graphs with bounded treewidth. Specifically, we prove that a graph is quasi-isometric to a graph with bounded tree…