Edge-trewidth: Algorithmic and combinatorial properties
Abstract
We introduce the graph theoretical parameter of edge treewidth. This parameter occurs in a natural way as the tree-like analogue of cutwidth or, alternatively, as an edge-analogue of treewidth. We study the combinatorial properties of edge-treewidth. We first observe that edge-treewidth does not enjoy any closeness properties under the known partial ordering relations on graphs. We introduce a variant of the topological minor relation, namely, the weak topological minor relation and we prove that edge-treewidth is closed under weak topological minors. Based on this new relation we are able to provide universal obstructions for edge-treewidth. The proofs are based on the fact that edge-treewidth of a graph is parametetrically equivalent with the maximum over the treewidth and the maximum degree of the blocks of the graph. We also prove that deciding whether the edge-treewidth of a graph is at most k is an NP-complete problem.
Cite
@article{arxiv.2112.07524,
title = {Edge-trewidth: Algorithmic and combinatorial properties},
author = {Loïc Magne and Christophe Paul and Abhijat Sharma and Dimitrios M. Thilikos},
journal= {arXiv preprint arXiv:2112.07524},
year = {2021}
}
Comments
22 pages, 10 figures