= Graph kernel
{title2=$K(G)$}
For a connected graph whose <2-core> contains a vertex of degree at least three, suppress each maximal path with degree-two internal vertices to a single edge, allowing its two endpoints to coincide. The resulting <multigraph>, retaining loops and parallel edges, is its kernel. Suppression preserves <graph excess> and leaves <minimum degree> at least three. A purely cyclic core is a separate unicyclic case; it has no branching vertex to anchor this construction.
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