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Infinite Euler Graphs

Published online by Cambridge University Press:  20 November 2018

Gert Sabidussi
Gert Sabidussi*
Affiliation:
McMaster University
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It is well known that for finite connected graphs the following are equivalent:

  1. (i) X is Euler (i.e., every vertex of X has positive even degree);

  2. (ii) X is traceable (i.e., the edges of X can be arranged in a sequence e1, . . . ,en such that ei ≠ ej if i ≠ j, and ei, ei+1 are adjacent, i = 1, . . . , n, subscripts considered mod n) ;

  3. (iii) X is cyclically coverable (i.e., X contains a family of non-overlapping circuits whose union is X).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 16 , 1964 , pp. 821 - 838
Copyright
Copyright © Canadian Mathematical Society 1964

References

1. Dirac, G. A., Note on the structure of graphs, Can. Math. Bull., 5 (1962), 221–227.Google Scholar
2. Erd, P.ös, T. Grunwald, and E. Vázsonyi, Über Euler-Linien unendlicher Graphen, J. Math. Phys., 17 (1938), 59–75.Google Scholar
3. König, D., Théorie der endlichen und unendlichen Graphen (Leipzig, 1936).Google Scholar
4. Ore, O., Theory of graphs, Amer. Math. Soc. Colloq. Publ., 88 (1962).Google Scholar