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- W2121217162 abstract "A n -vertex graph is said to be decomposable if for any partition ( λ 1 , … , λ p ) of the integer n , there exists a sequence ( V 1 , … , V p ) of connected vertex-disjoint subgraphs with | V i | = λ i . In this paper, we focus on decomposable trees. We show that a decomposable tree has degree at most 4. Moreover, each degree-4 vertex of a decomposable tree is adjacent to a leaf. This leads to a polynomial time algorithm to decide if a multipode (a tree with only one vertex of degree greater than 2) is decomposable. We also exhibit two families of decomposable trees: arbitrary large trees with one vertex of degree 4, and trees with an arbitrary number of degree-3 vertices." @default.
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- W2121217162 date "2006-03-01" @default.
- W2121217162 modified "2023-09-25" @default.
- W2121217162 title "A degree bound on decomposable trees" @default.
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- W2121217162 doi "https://doi.org/10.1016/j.disc.2006.01.006" @default.
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