Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic
tractability: if the clique-width of a graph class G is bounded by a constant, a wide range of …

The Grid Theorem for vertex-minors - ScienceDirect Skip to main contentSkip to article Elsevier
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This thesis is about a conjecture of Geelen on the structure of graphs with a forbidden vertex-
minor; the conjecture is like the Graph Minors Structure Theorem of Robertson and Seymour …

Given an infinite word over the alphabet $\{0, 1, 2, 3\} $, we define a class of bipartite
hereditary graphs $\mathcal {G}^\alpha $, and show that $\mathcal {G}^\alpha $ has …

We discover new hereditary classes of graphs that are minimal (with respect to set inclusion)
of unbounded clique-width. The new examples include split permutation graphs and bichain …

Seese's conjecture for finite graphs states that monadic second-order logic (MSO) is
undecidable on all graph classes of unbounded clique-width. We show that to establish this …

It has long been known that the following basic objects are obstructions to bounded tree-
width: for arbitrarily large t,(1) the complete graph K t,(2) the complete bipartite graph K t, t,(3) …

We create a framework for hereditary graph classes built on a two-dimensional grid of
vertices and edge sets defined by a triple of objects that define edges between consecutive …

We consider hereditary classes of bipartite graphs where clique-width is bounded, but linear
clique-width is not. Our goal is identifying classes that are critical with respect to linear clique …

In the study of graphs, clique-width is a parameter that has received much attention due its
significance in the tractability of algorithms on certain classes of graph. Of particular interest …