Abstract
A tree decomposition of graphG = (V, E) is referred to as a partition of edge setE into edge-disjoint trees. Given (not necessarily distinct) vertices u1, u2 ⋯ uk∈V with k⩾2, a sufficient and necessary condition is given for a connected graphG = (V, E) to have a tree decompositionT 1,T 2⋯T k such thatV(T 1)=V i,i=1, 2, ⋯ k.
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Yuan, X., Cai, M. Tree decomposition. Chin. Sci. Bull. 43, 1599–1601 (1998). https://doi.org/10.1007/BF02883401
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DOI: https://doi.org/10.1007/BF02883401