Random 4-regular graphs have claw-decompositions asymptotically almost surely
نویسندگان
چکیده
In 2006, Barát and Thomassen conjectured that the edges of every planar 4-regular 4-edgeconnected graph can be decomposed into claws. Shortly afterward, Lai constructed a counterexample to this conjecture. Using the small subgraph conditioning method of Robinson and Wormald, we find that a random 4-regular graph has a claw-decomposition asymptotically almost surely, provided that the number of vertices is divisible by 3.
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