## Figures from this paper

## 11 Citations

Ks,t Minors in (s+t) ‐ Chromatic Graphs, II

- MathematicsJ. Graph Theory
- 2014

It is shown that the statement holds already for much smaller t, namely, for t>Cslogs3, and confirmed a partial case of the corresponding conjecture by Woodall and Seymour.

Defective Colouring of Graphs Excluding A Subgraph or Minor

- MathematicsComb.
- 2019

A common generalisation of these theorems with a weaker assumption about excluded subgraphs is proved, which leads to new defective colouring results for several graph classes, including graphs with linear crossing number, graphs with given thickness, and graphs excluding a complete bipartite graph as a topological minor.

Forcing a sparse minor

- MathematicsCombinatorics, Probability and Computing
- 2015

The main result, which complements the result of Myers and Thomason, states that if H has t vertices and average degree d at least some absolute constant, then f(H) ≤ 3.895\sqrt{\ln d}\,t$ .

Average Degree Conditions Forcing a Minor

- MathematicsElectron. J. Comb.
- 2016

This work strengthens (under certain conditions) a recent result by Reed and Wood, giving better bounds on the average degree required to force an arbitrary graph as a minor when $H$ is a sparse graph with many high degree vertices.

Disproof of a Conjecture by Woodall

- Mathematics
- 2022

In 2001, in a survey article [26] about list coloring, Woodall conjectured that for every pair of integers s, t ≥ 1, all graphs without a Ks,t-minor are (s + t − 1)-choosable. In this note we refute…

A Lower Bound on the Average Degree Forcing a Minor

- Mathematics, Computer ScienceElectron. J. Comb.
- 2020

It is shown that for sufficiently large graphs and for t ≥ d, there is a graph G such that almost every graph H with t vertices and average degree $H$ is not a minor of $G$, where $\lambda=0.63817\dots$ is an explicitly defined constant.

The extremal function for structured sparse minors

- Mathematics
- 2021

Let c(H) be the smallest value for which e(G)/|G| > c(H) implies H is a minor of G. We show a new upper bound on c(H), which improves previous bounds for graphs with a vertex partition where some…

On Treewidth and Graph Minors

- Mathematics, Computer Science
- 2014

This thesis determines exactly the treewidth of the line graph of a complete graph, up to lower order terms in general, and exactly whenever the complete multipartite graph is regular, and generalises a result by Lucena.

Hadwiger's Conjecture

- MathematicsOpen Problems in Mathematics
- 2016

This is a survey of Hadwiger’s conjecture from 1943, that for all t ≥ 0, every graph either can be t-coloured, or has a subgraph that can be contracted to the complete graph on t + 1 vertices. This…

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