Random d-regular graphs a.a.s. have k-star decompositions with s or s+1 stars per vertex for all k < d/2 - 1, with prescribed star centers when k is sufficiently small.
Decomposing random regular graphs into stars.arXiv, (2308.16037), 2023
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Star decompositions via orientations
Random d-regular graphs a.a.s. have k-star decompositions with s or s+1 stars per vertex for all k < d/2 - 1, with prescribed star centers when k is sufficiently small.