Regular Article
Undecidability of Winkler′s r-Neighborhood Problem for Covering Digraphs

https://doi.org/10.1006/jctb.1994.1017Get rights and content
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Abstract

Consider the following decision problem which P. Winkler and V. Bulitko (independently) showed was undecidable: Given a finite set Φ of rooted graphs and a positive integer r, is there a graph G such that Φ represents, up to isomorphism, the set of all r-neighborhoods of G? We show the undecidability of the related problem in which G is required to be the covering digraph of a partial ordering. Our construction shows that the problem remains undecidable (for certain fixed r) even when G is also required to be planar and bipartite.

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