Factorization of the Green's operator and weak-type estimates for a random walk on a tree.
Finding a spanning tree of a graph with maximal number of terminal vertices
Finding Minimal Branchings With a Given Number of Arcs
Fixed point theorems in CAT(0) spaces and -trees.
Forest decompositions of graphs with cyclomatic number 2.
Forest decompositions of graphs with cyclomatic number 3.
From paths to stars.
Front-divisors of trees.
Functions on adjacent vertex degrees of trees with given degree sequence
In this note we consider a discrete symmetric function f(x, y) where associated with the degrees of adjacent vertices in a tree. The extremal trees with respect to the corresponding graph invariant, defined as are characterized by the “greedy tree” and “alternating greedy tree”. This is achieved through simple generalizations of previously used ideas on similar questions. As special cases, the already known extremal structures of the Randic index follow as corollaries. The extremal structures...