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On Equi-Cardinal, Restrictions of a Graph

Published online by Cambridge University Press:  20 November 2018

J. C. Beatty  and
R. E. Miller
J. C. Beatty
Affiliation:
I.B.M.Yorktown HeightsN.Y.
R. E. Miller
Affiliation:
I.B.M.Yorktown HeightsN.Y.
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A graph G is an ordered pair (V, E) where V is a set of objects called vertices, and E is a set of unordered pairs of vertices (v, v') in which each such pair can occur at most once in E, and if (v, v') ϵ E then v ≠ v'. The order of G is the cardinality of the set V, and the degree δ(v) of an element v ϵ V is the number of elements of E which contain v. G is said to be regular of degree d if δ(v) = d for each v ϵ V. G is a complete graph if E contains every pair of elements of V. A graph H = (V', E') is a partial graph of G=(V, E) if V' ⊆ v and E' ⊆ E. H is a restriction of G if H is a partial graph of G in which V' = V. Let S = { e1, …, el} be a subset of E such that ej={vj-1, vj} for 1 ≤j ≤l.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 7 , Issue 3 , September 1964 , pp. 369 - 375
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Tutte, W. T., The Factors of a Graph, Canad. J. Math. 4, 1952, pp. 314–328.Google Scholar
2. Ore, Oystein, Theory of Graphs, AMS, 1962.Google Scholar