Extremal problems for trees with given segment sequence
نویسندگان
چکیده
منابع مشابه
Counting labelled trees with given indegree sequence
For a labelled tree on the vertex set [n] := {1, 2, . . . , n}, define the direction of each edge ij to be i → j if i < j. The indegree sequence of T can be considered as a partition λ ⊢ n − 1. The enumeration of trees with a given indegree sequence arises in counting secant planes of curves in projective spaces. Recently Ethan Cotterill conjectured a formula for the number of trees on [n] with...
متن کاملKeywords. Davenport{schinzel Sequence; Tree; Extremal Problem 0 Extremal Problems for Colored Trees and Davenport{schinzel Sequences
In the theory of generalized Davenport{Schinzel sequences one estimates the maximum lengths of nite sequences containing no subsequence of a given pattern. Here we investigate a further generalization, in which the class of sequences is extended to the class of colored trees. We determine exactly the extremal functions associated with the properly 2-colored path of four vertices and with the mo...
متن کاملThe Number of Subtrees of Trees with Given Degree Sequence
This article investigates some properties of the number of subtrees of a tree with given degree sequence. These results are used to characterize trees with the given degree sequence that have the largest number of subtrees, which generalize the recent results of Kirk and Wang (SIAM J Discrete Math 22 (2008), 985–995). These trees coincide with those which were proven by Wang and independently Z...
متن کاملA bijective enumeration of labeled trees with given indegree sequence
For a labeled tree on the vertex set {1, 2, . . . , n}, the local direction of each edge (i j) is from i to j if i < j. For a rooted tree, there is also a natural global direction of edges towards the root. The number of edges pointing to a vertex is called its indegree. Thus the local (resp. global) indegree sequence λ = 1e2e . . . of a tree on the vertex set {1, 2, . . . , n} is a partition o...
متن کاملThe ABC Index of Trees with Given Degree Sequence∗
The atom–bond connectivity index of a graph G is defined as
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2017
ISSN: 0166-218X
DOI: 10.1016/j.dam.2016.12.009