A Flat Wall Theorem for Matching Minors in Bipartite Graphs

by   Archontia C. Giannopoulou, et al.

A major step in the graph minors theory of Robertson and Seymour is the transition from the Grid Theorem which, in some sense uniquely, describes areas of large treewidth within a graph, to a notion of local flatness of these areas in form of the existence of a large flat wall within any huge grid of an H-minor free graph. In this paper, we prove a matching theoretic analogue of the Flat Wall Theorem for bipartite graphs excluding a fixed matching minor. Our result builds on a a tight relationship between structural digraph theory and matching theory and allows us to deduce a Flat Wall Theorem for digraphs which substantially differs from a previously established directed variant of this theorem.



There are no comments yet.


page 35


A more accurate view of the Flat Wall Theorem

We introduce a supporting combinatorial framework for the Flat Wall Theo...

Quickly excluding a non-planar graph

A cornerstone theorem in the Graph Minors series of Robertson and Seymou...

Cyclewidth and the Grid Theorem for Perfect Matching Width of Bipartite Graphs

A connected graph G is called matching covered if every edge of G is con...

On the tree-width of even-hole-free graphs

The class of all even-hole-free graphs has unbounded tree-width, as it c...

Towards Tight(er) Bounds for the Excluded Grid Theorem

We study the Excluded Grid Theorem, a fundamental structural result in g...

Reducing Topological Minor Containment to the Unique Linkage Theorem

In the Topological Minor Containment problem (TMC) problem two undirecte...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.