Tree decompositions of graphs are of fundamental importance in structural and algorithmic graph theory. Planar decompositions generalise tree decompositions by allowing an arbitrar...
We develop new structural results for apex-minor-free graphs and show their power by developing two new approximation algorithms. The first is an additive approximation for colorin...
Erik D. Demaine, MohammadTaghi Hajiaghayi, Ken-ich...
We show how to view certain subclasses of (single-pushout) graph transformation systems as well-structured transition systems, which leads to decidability of the covering problem v...
We first prove that for any fixed k a cubic graph with few short cycles contains a Kk-minor. This is a direct generalisation of a result on girth by Thomassen. We then use this the...
We prove that fixed-point logic with counting captures polynomial time on all classes of graphs with excluded minors. That is, for every class C of graphs such that some graph H is...