An Overview of Universal Obstructions for Graph Parameters
Discrete Mathematics
2026-05-04 v3 Combinatorics
Abstract
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering on graphs. Towards this, we proposed the concepts of class obstruction, parametric obstruction, and universal obstruction as combinatorial objects that determine the approximate behaviour of a graph parameter. In this work, we explore its potential as a unifying framework for classifying graph parameters. Under this framework, we survey existing graph-theoretic results on many known graph parameters. Additionally, we provide some unifying results on their classification.
Keywords
Cite
@article{arxiv.2304.14121,
title = {An Overview of Universal Obstructions for Graph Parameters},
author = {Christophe Paul and Evangelos Protopapas and Dimitrios M. Thilikos},
journal= {arXiv preprint arXiv:2304.14121},
year = {2026}
}