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arXiv · 2304.14121

An Overview of Universal Obstructions for Graph Parameters

Christophe Paul·Evangelos Protopapas·Dimitrios M. Thilikos
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Abstract

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.

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Christophe Paul, Evangelos Protopapas, Dimitrios M. Thilikos. 2023-04-27. An Overview of Universal Obstructions for Graph Parameters. https://arxiv.org/abs/2304.14121

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