A new and simple proof is given of the known theorem that, if T 1 , T 2, … , is an infinite sequence of finite trees, then there exist i and j such that i < j and T i is homeomorphic to a subtree of… Expand

1. I n t r o d u c t i o n . The integer par t of a non-negative real number p will be denoted by [p]. For any integer ny n* will denote the greatest even integer less than or equal to n, t h a t is,… Expand

Let G be a locally finite connected graph and c be a positive real-valued function defined on its edges. Let D (ξ) denote the sum of the values of c on the edges incident with a vertex ξ. A particle… Expand

. Let Q be a well-quasi-ordered set, i.e. a set on which a reflexive and transitive relation ≤ is defined and such that, for every infinite sequence q 1 , q 2 ,… of elements of Q , there exist i and… Expand

We find necessary and sufficient conditions for G to have a detachment F without loops or multiple edges such that F is a complete graph with 2r + 1 vertices and F(Ei) is a Hamilton circuit of F for i = 1, …, r.Expand

On considere des graphes finis qui peuvent avoir des boucles et des aretes multiples. On definit les notions de detachement d'un graphe et des queues d'Euler generalisees