Random 4-regular graphs have 3-star decompositions asymptotically almost surely
2018
Abstract Barat and Thomassen conjectured in 2006 that the edges of every planar 4-regular 4-edge-connected graph can be decomposed into copies of the star with 3 leaves. Shortly afterward, Lai constructed a
counterexampleto this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we prove that a random 4-
regular graphhas an S 3 -decomposition asymptotically
almost surely, provided the number of vertices is divisible by 3.
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