18 citations · 62 across the 29 of their papers we have counts for
3 papers · 1 filter
Asymptotic dimension of graphs excluding an induced or fat minor
Robert Hickingbotham, Freddie Illingworth, Piotr Micek +1
Asymptotic dimension is a large-scale invariant of metric spaces that was introduced by Gromov (1993). A major open problem in coarse graph theory asks whether, for every fixed gra…
Induced Forest Minor Theorem for Graphs Without an Induced Star
Robert Hickingbotham, Gwenaël Joret
Motivated by recent work on tree independence number, we study the path independence number of a graph : the minimum integer such that there is a path decomposition of w…
Optimal tree-decompositions with bags of bounded pathwidth
Kevin Hendrey, Robert Hickingbotham, Jędrzej Hodor +1
We show that every planar graph has a tree-decomposition with optimal width such that the subgraph induced by each bag has pathwidth at most 3. This bound is best possible, and for…