OEIS A000314: Hussemi trees and polygonal cacti sequences

An in-depth look at OEIS A000314: the number of mixed Hussemi trees, i.e., labeled polygonal cacti with bridges. We clarify cactus graphs, blocks that are edges or cycles, and the historical name Hussemi trees, then connect these structures to outer-planar graphs and discuss why many problems become polynomial on cactus graphs. We also explore real-world applications in circuits and comparative genomics, and highlight the triangular-cactus case tied to Rosa's conjecture on graph labelings.

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