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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

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2. Egyed, L., Ueber die wohlgerichteten unendlichen Graphen, Math. phys. Lapok, 48 (1941), 505–509.(Hungarian with German summary).Google Scholar
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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