For s-embeddable edge-color-critical F with the stated edge correction, spectral extremal non-r-partite F-free graphs are unique and edge-extremal; complete multipartite cases are fully classified.
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A reduction principle for non-$r$-partite spectral extremal problems, with a complete multipartite classification
For s-embeddable edge-color-critical F with the stated edge correction, spectral extremal non-r-partite F-free graphs are unique and edge-extremal; complete multipartite cases are fully classified.