Vol. 23, No. 3, 1967

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A necessary condition for d-polyhedrality

David Wilmot Barnette

Vol. 23 (1967), No. 3, 435–440

A graph is d-polyhedral provided it is isomorphic to the graph of a d-dimensional convex polytope. One of the unsolved problems in the field of convex polytopes is to characterize the d-polyhedral graphs for d > 3. There are, however, several necessary conditions known for a graph to be d-polyhedral. In this paper we present a new necessary condition which is not implied by the other conditions but which has two of them as corollaries. We also show how this new condition may be useful in solving problems dealing with ambiguity of d-polyhedral graphs.

Mathematical Subject Classification
Primary: 05.50
Secondary: 52.00
Received: 21 February 1967
Published: 1 December 1967
David Wilmot Barnette