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Some Properties of Graphs with Multiple Edges

Published online by Cambridge University Press:  20 November 2018

D. R. Fulkerson ,
A. J. Hoffman  and
M. H. McAndrew
D. R. Fulkerson
Affiliation:
RAND Corporation and IBM Research Center
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In this paper we consider undirected graphs, with no edges joining a vertex to itself, but with possibly several edges joining pairs of vertices. The first part of the paper deals with the question of characterizing those sets of non-negative integers d1d2 . . . , dn and {cij}, 1 ≤ i < j ≤ n, such that there exists a graph G with n vertices whose valences (degrees) are the numbers di, and with the additional property that the number of edges joining i and j is at most cij. This problem has been studied extensively, in the general case (1, 2, 9, 11), in the case where the graph is bipartite (3, 5, 7, 10), and in the case where the Cij are all 1 (6).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 166 - 177
Copyright
Copyright © Canadian Mathematical Society 1965

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