Counting branches in trees using games

Counting Branches in Trees Using Games

We study finite automata running over infinite binary trees. A run of such an automaton is usually said to be accepting if all its branches are accepting. In this article, we relax the notion of accepting run by allowing a certain quantity of rejecting branches. More precisely we study the following criteria for a run to be accepting: (i) it contains at most finitely (resp. countably) many reje...

Branches in random recursive k-ary trees

In this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. We also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Counting Trees Using Symmetries

Counting spanning trees using modular decomposition

In this paper we present an algorithm for determining the number of spanning trees of a graph G which takes advantage of the structure of the modular decomposition tree of G. Specifically, our algorithm works by contracting the modular decomposition tree of the input graph G in a bottom-up fashion until it becomes a single node; then, the number of spanning trees of G is computed as the product...

Counting Trees

Let t n denote the number of unlabeled trees on n vertices. Let t(x) = P 1 n=1 t n x n be the corresponding generating function. Similarly, let T n , h n , and i n denote the numbers of rooted trees, homeomorphically irreducible trees, and identity trees on n vertices, respectively. (Homeomorphically irre-ducible trees have no vertices of degree 2, and identity trees have trivial au-tomorphism ...