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On well-quasi-ordering finite trees
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 ofExpand
On orientations, connectivity and odd-vertex-pairings in finite graphs.
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
Random walk and electric currents in networks
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 particleExpand
On well-quasi-ordering transfinite sequences
. 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 andExpand
Amalgamations of almost regular edge-colourings of simple graphs
  • C. Nash-Williams
  • Computer Science, Mathematics
  • J. Comb. Theory, Ser. B
  • 1 December 1986
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
Connected detachments of graphs and generalized Euler trails
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