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A Note on Undirected Graphs Realizable as P.O. Sets

Published online by Cambridge University Press:  20 November 2018

C. E. Haff ,
U. S. R. Murty  and
R. C. Wilton
C. E. Haff
Affiliation:
University of Waterloo, Waterloo, Ontario
U. S. R. Murty
Affiliation:
University of Waterloo, Waterloo, Ontario
R. C. Wilton
Affiliation:
University of Waterloo, Waterloo, Ontario
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Let (P, ≥) be a p.o. set. The basis graph of (P, ≥) is defined to be the directed graph whose vertex set is P and in which the ordered pair 〈a, b〉 is an edge if and only if b covers a in (P, ≥).

Let D be a directed graph. All graphs considered in this note are finite and are free of loops and multiple edges.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 13 , Issue 3 , September 1970 , pp. 371 - 374
Copyright
Copyright © Canadian Mathematical Society 1970

References

1. Alvarez, L. R., Undirected graphs realizable as graphs of modular lattices, Can. J. Math. 17 (1965), 923-32.Google Scholar
2. Ore, O., Theory of graphs, Providence, R.I., 1962.Google Scholar
3. Ore, O., The four-color problem, Academic Press, New York, 1967.Google Scholar