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The Decomposition of Graphs into a Finite Number of Paths

Published online by Cambridge University Press:  20 November 2018

Bruce Rothschild
Bruce Rothschild*
Affiliation:
Yale University
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In (3) Ore poses two problems concerning the decomposition of graphs into edge-disjoint paths. The first is to find the conditions on a graph so that it can be decomposed into a finite number k of edge-disjoint, two-way infinite paths and no fewer. In (2) Nash-Williams solves this problem. The results of (2) are used here to solve the second problem, to find conditions on a graph so that it can be decomposed into a finite number k of edge-disjoint paths (finite, one-way infinite, and two-way infinite) and no fewer.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 17 , 1965 , pp. 468 - 479
Copyright
Copyright © Canadian Mathematical Society 1965

References

1. Erdös, P., Grunwald, T., and E. Vàzsonyi, Über Euler-Linien unendlicher Graphen, J. Math. Phys., 17 (1938), 59–75.Google Scholar
2. Nash-Williams, C. St. J. A., Decomposition of graphs into two-way infinite paths, Can. J. Math., 15 (1963), 479–85.Google Scholar
3. Ore, O., Theory of graphs (Providence, 1962).Google Scholar