New classes of graphs with strongly almost trivial embeddings (Q6638256)

The author explores new classes of graphs with strongly almost trivial (\( SAT\)) embeddings, contributing to the study of spatial graphs. Theorems for specific structures, like \(G(m_1,m_2,\dots,m_k)\) with even multiplicities and \(G_n\) with multiple edges and loops, demonstrate SAT embeddings through constructions and projections. Color invariants and irreducibility theorems support their nontriviality. The paper also raises open questions about SAT embeddings in other graph families.