Awesome graph parameters
Kenny Be\v{s}ter \v{S}torgel, Cl\'ement Dallard, Vadim Lozin, Martin Milani\v{c}, Viktor Zamaraev

TL;DR
This paper explores the relationship between graph parameters related to independent sets and cliques, classifying them as 'awesome' or 'awful' based on their boundedness properties and implications for graph classes.
Contribution
It introduces the concepts of 'awesome' and 'awful' parameters, identifies several parameters fitting these categories, and discusses their algorithmic and theoretical implications.
Findings
Identified several 'awesome' graph parameters.
Established criteria for 'awesomeness' and 'awfulness' of parameters.
Proposed open problems and applications related to these classifications.
Abstract
For a graph , we denote by the size of a maximum independent set and by the size of a maximum clique in . Our paper lies on the edge of two lines of research, related to and , respectively. One of them studies -variants of graph parameters, such as -treewidth or -degeneracy. The second line deals with graph classes where some parameters are bounded by a function of . A famous example of this type is the family of -bounded classes, where the chromatic number is bounded by a function of . A Ramsey-type argument implies that if the -variant of a graph parameter is bounded by a constant in a class , then is bounded by a function of in . If the reverse implication also holds, we say that is awesome. Otherwise, we say…
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · Topological and Geometric Data Analysis
