20 citations · 52 across the 17 of their papers we have counts for
31 papers · 1 filter
Every graph with no minor is 6-colorable
Zdeněk Dvořák, Sergey Norin, Neil Rahman
The first open case of Hadwiger's conjecture states that every -minor-free graph is 6-colorable. We prove that this is the case for -minor-free graphs, where de…
Two Relaxations of the Dominating Hadwiger's Conjecture
António Girão, Sergey Norin, Youri Tamitegama +1
Illingworth and Wood recently proposed the Dominating Hadwiger's Conjecture, a strengthening of Hadwiger's Conjecture which asserts that every graph with no dominating -model…
Nerve-type and invariance theorems for asymptotic dimension
Chun-Hung Liu, Sergey Norin
Asymptotic dimension of metric spaces is a large-scale analog of covering dimension of topological spaces. An intersection graph of a family of sets is the graph whose vertices are…
The Dominating 4-Colour Theorem
António Girão, Freddie Illingworth, Bojan Mohar +6
A "dominating -model" in a graph is a sequence of pairwise vertex-disjoint connected subgraphs of , such that whenever every vertex…
Every graph with no -minor is -colorable
Sergey Norin, Agnes Totschnig
Let denote the graph obtained from the complete graph on seven vertices by deleting two edges with a common end. Motivated by Hadwiger's conjecture, we prove that ever…
3-Colouring Planar Graphs
Vida Dujmović, Pat Morin, Sergey Norin +1
We show that every -vertex planar graph is 3-colourable with monochromatic components of size . The best previous bound was due to Linial, Matoušek, She…