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 …

We show that for every fixed k, there is a linear time algorithm that decides whether or not a
given graph has a vertex set X of order at most k such that GX is planar (we call this class of …

A key theorem in algorithmic graph-minor theory is a min-max relation between the treewidth
of a graph and its largest grid minor. This min-max relation is a keystone of the Graph Minor …

At the core of the Robertson-Seymour theory of graph minors lies a powerful decomposition
theorem which captures, for any fixed graph H, the common structural features of all the …

In this paper, we consider optimal 1-planar multigraphs, that is, n-vertex multigraph having
exactly 4 n− 8 edges and a drawing on the sphere such that each edge crosses at most one …

Excluding a small minor - ScienceDirect Skip to main contentSkip to article Elsevier logo
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At the core of the Robertson–Seymour theory of graph minors lies a powerful structure
theorem which captures, for any fixed graph H, the common structural features of all the …

A Characterization of Graphs with No Octahedron Minor - Ding - 2013 - Journal of Graph Theory
- Wiley Online Library Skip to Article Content Skip to Article Information Wiley Online Library …

The famous Hadwiger's conjecture asserts that every graph with no Kt-minor is (t-1)-
colorable. The case t= 5 is known to be equivalent to the Four Color Theorem by Wagner …

A key theorem in algorithmic graph-minor theory is a min-max relation between the treewidth
of a graph (ie, the minimum width of a tree-decomposition) and the maximum size of a grid …