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Graphs Orientable as Distributive Lattices

Dwight Duffus and Ivan Rival
Proceedings of the American Mathematical Society
Vol. 88, No. 2 (Jun., 1983), pp. 197-200
DOI: 10.2307/2044697
Stable URL: http://www.jstor.org/stable/2044697
Page Count: 4
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Graphs Orientable as Distributive Lattices
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Abstract

There are two types of graphs commonly associated with finite (partially) ordered sets: the comparability graph and the covering graph. While the first type has been characterized, only partial descriptions of the second are known. We prove that the covering graphs of distributive lattices are precisely those graphs which are retracts of hypercubes.

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