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• W1570587257 abstract "Greedy trees are constructed from a given degree sequence by a simple greedy algorithm that assigns the highest degree to the root, the second-, third-, ... highest degrees to the root's neighbors, and so on. They have been shown to maximize or minimize a number of different graph invariants among trees with a given degree sequence. In particular, the total number of subtrees of a tree is maximized by the greedy tree. In this work, we show that in fact a much stronger statement holds true: greedy trees maximize the number of subtrees of any given order. This parallels recent results on distance-based graph invariants. We obtain a number of corollaries from this fact and also prove analogous results for related invariants, most notably the number of antichains of given cardinality in a rooted tree." @default.
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• W1570587257 date "2013-08-30" @default.
• W1570587257 modified "2023-10-14" @default.
• W1570587257 title "Greedy Trees, Subtrees and Antichains" @default.
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• W1570587257 doi "https://doi.org/10.37236/3101" @default.
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