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Some uniqueness results for upper bound

✍ Scribed by F.R. McMorris; G.T. Myers

Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
162 KB
Volume
44
Category
Article
ISSN
0012-365X

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✦ Synopsis

The upper bound graphs that arise from exactly one (up to isomorphism) poser :~rc characterized. Weakening these conditions, the class of graphs whose intersection number is equal to the independence number is characterized.

In this note all sets are finite and all graphs are connected, undirected, and without loops or multiple edges. If (P, ~<) is a partially ordered set (poset), then the upper bound graph of P, G = (V, E), is defined as follows: V = P and xy e E if and only if x ~ y and there exists z s P such that x, y -<.-z. We say that P realizes its upper bound graph, and that a graph G is an upper bound graph (UB-graph) if there is a poset that realizes G.

We recall a result found in .

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