On Edge-Decomposition of Cubic Graphs into Copies of the Double-Star with Four Edges
A tree containing exactly two non-pendant vertices is called a double-star. Let k_1 and k_2 be two positive integers. The double-star with degree sequence (k_1+1, k_2+1, 1, ldots, 1) is denoted by S_{k_1, k_2}. It is known that a cubic graph has an S_{1,1}-decomposition if and only if it contains a perfect matching. In this paper, we study the S_{1,2}-decomposition of cubic graphs. We present some necessary and some sufficient conditions for the existence of an S_{1, 2}-decomposition in cubic graphs.
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