Some Properties of Graphs with Multiple Edges
Some Properties of Graphs with Multiple Edges
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DOI：
10.4153/cjm-1965-016-2
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发表时间：
1965
期刊：
影响因子：
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通讯作者：
D. R. Fulkerson;A. Hoffman;M. Mcandrew
中科院分区：
文献类型：
--
作者：
D. R. Fulkerson;A. Hoffman;M. Mcandrew
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 d 1 d 2 . . . , 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).
