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Despite this result, few graphs have been constructed which exhibit the property P(m,n,k)... We begin by stating the following two

N. The problem that arises is that of characterizing k-extendable and minimally k-extendable graphs. k-extendable graphs have been studied by a number of authors

Gliviak, On Certain Classes of Graphs of Diameter Two without Superfluous Edges, Acta F.R.N. Gliviak, On Certain Edge-Critical Graphs of Given Diameter,

Many problems concerning matchings and deficiency in graphs have been investigated in the literature - see, for example Lovasz and Plummer [6].. This bound is

Over the past twenty years or so there has been considerable interest in the problem of partitioning the edge set of a graph into disjoint Hamilton cycles

Bollobas and Eldridge [2] considered the problem of determining the minimum possible of maximium matching of a graph G with prescribed minimum maximum degrees

Equality is achieved just if every face is doubly braced: Lemmas 4 and 5 show this happens if and only if T results from triangulating every face of some lower order

Kn denotes the complete graph on n vertices m denotes the complete bipartite graph with bipartitioning sets of size nand m... In this paper we generalize these