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Decomposition of Graphs into Two-Way Infinite Paths

Published online by Cambridge University Press:  20 November 2018

C. ST. J. A. Nash-Williams
C. ST. J. A. Nash-Williams*
Affiliation:
University of A berdeen
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We consider undirected graphs in which two vertices may be joined by more than one edge and in which a vertex may be joined to itself by one or more edges. G will always denote a graph. The set of vertices [edges] of G will be denoted by V(G) [E(G)]. G is finite or infinite according as V(G) ∪ E(G) is finite or infinite. The degree, d(ξ) or dG(ξ), of a vertex ξ of G is 2a + b, where a is the number of edges joining ξ to itself and b is the number of those joining ξ to other vertices.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 15 , 1963 , pp. 479 - 485
Copyright
Copyright © Canadian Mathematical Society 1963

References

1. St, C.. J. A. Nash-Williams, Decomposition of graphs into closed and endless chains, Proc London Math. Soc. (3), 10 (1960), 221–238.Google Scholar
2. St, C.. Nash-Williams, J. A., Decomposition of graphs into infinite chains (thesis, Cambridge, 1958).Google Scholar
3. Ore, O., Theory of graphs (Providence, 1962).Google Scholar