Invariant systems of representatives, or The cost of symmetry

TL;DR

This paper investigates the minimal invariant edge removal needed to eliminate all 100-gons in a graph, exploring the interplay between symmetry and graph modification, and providing solutions to these symmetry-constrained problems.

Contribution

It introduces methods to determine the minimal invariant edge sets required to destroy all 100-gons, addressing symmetry constraints in graph modification problems.

Findings

Established bounds for invariant edge removal in graphs with 100-gons.

Provided explicit solutions for specific graph classes.

Raised open questions on symmetry and graph invariants.

Abstract

Suppose that one can destroy all 100-gons in a graph by removing 2019 edges. How many edges must be removed to destroy all 100-gons in such a way that the set of removed edges is invariant with respect to all automorphisms the initial graph? This paper contains solutions to such kind of problems. Several open questions are raised.