The content discusses the complexity of graph isomorphism testing, focusing on graphs excluding specific subgraphs. It introduces a novel algorithm that significantly improves previous methods by leveraging group-theoretic techniques and closure operators. The approach involves decomposing input graphs into parts with simple interplay, leading to efficient isomorphism testing. The study provides structural insights into automorphism groups of such graphs, highlighting their unique properties.
The theorem presented in the content establishes a key technical contribution by demonstrating how to compute suitable initial sets for isomorphism testing. By utilizing the 3-dimensional Weisfeiler-Leman algorithm, the author proves that these initial sets satisfy essential properties required for efficient graph analysis. The proof involves intricate analyses of colorings and closure operators to ensure isomorphism-invariance.
Overall, the content delves deep into the theoretical aspects of graph isomorphism testing, offering innovative solutions for challenging problems in computational complexity theory.
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