All regular multigraphs of even order and high degree are 1-factorable.
Vertex-oriented Hamilton cycles in directed graphs.
Minimum maximal graphs with forbidden subgraphs
On Decomposing Regular Graphs Into Isomorphic Double-Stars
A double-star is a tree with exactly two vertices of degree greater than 1. If T is a double-star where the two vertices of degree greater than one have degrees k1+1 and k2+1, then T is denoted by Sk1,k2 . In this note, we show that every double-star with n edges decomposes every 2n-regular graph. We also show that the double-star Sk,k−1 decomposes every 2k-regular graph that contains a perfect matching.
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