An Overview of Universal Obstructions for Graph Parameters
For graph theorists, this work offers a unifying framework to understand and classify graph parameters, but it is primarily a survey with some new unifying results.
The paper introduces a parametric framework for classifying graph parameters using obstruction characterizations, surveying existing results and providing unifying classification results.
In a recent work, we introduced a parametric framework for obtaining obstruction characterizations of graph parameters with respect to a quasi-ordering $\leqslant$ 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.