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On Orientations, Connectivity and Odd-Vertex-Pairings in Finite Graphs

Published online by Cambridge University Press:  20 November 2018

C. ST. J. A. Nash-Williams
C. ST. J. A. Nash-Williams*
Affiliation:
University of Aberdeen
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The integer part of a non-negative real number p will be denoted by [p]. For any integer n, n* will denote the greatest even integer less than or equal to n, that is, n* = n or n — 1 according as n is even or odd respectively.

The order of a set A, denoted by |A|, is the number of elements in A. The set whose elements are a1, a2, … , an will be denoted by {a1, a2 … , an. The empty set will be denoted by Λ. A set will be said to include each of its elements. A set separates two elements if it includes one but not both of them.

An unoriented graph U consists of two disjoint sets V(U), E(U), the elements of V(U) being called vertices of U and the elements of V(U) being called edges of U, together with a relationship whereby with each edge is associated an unordered pair of distinct vertices which the edge is said to join.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 12 , 1960 , pp. 555 - 567
Copyright
Copyright © Canadian Mathematical Society 1960

References

1. Cantoni, R., Conseguenze dell’ ipotesi del circuito totale pari per le reti con vertici tripli, R. C. 1st. lombardo, Classe di Scienze Matematiche e Naturali (3), 14 (83) (1950), 371–387.Google Scholar
2. Egyed, L., Ueber die wohlgerichteten unendlichen Graphen, Math. phys. Lapok, 48 (1941), 505–509.(Hungarian with German summary).Google Scholar
3. König, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936; reprinted New York, 1950).Google Scholar
4. Robbins, H.E., A theorem on graphs, with an application to a problem of traffic control, Amer. Math. Monthly, 40 (1939), 281–3.Google Scholar