We solve an open problem posed by Eppstein in 1995 [14, 15] and re-enforced by Grohe [16, 17] concerning locally bounded treewidth in minor-closed families of graphs. A graph has ...
We prove that local complementation and vertex deletion, operations from which vertexminors are defined, can simulate edge contractions. As an application, we prove that the rank...
A tree decomposition of the coordinates of a code is a mapping from the coordinate set to the set of vertices of a tree. A tree decomposition can be extended to a tree realization,...
ABSTRACT. A graphical realization of a linear code C consists of an assignment of the coordinates of C to the vertices of a graph, along with a specification of linear state spaces...
This tutorial will present an overview of the use of Monadic Second-Order Logic to describe sets of finite graphs and graph transformations, in relation with the notions of tree-w...