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A pair of graphs (G 1 ,G 2 ) on the same set of vertices V is called bound polysemic, if there is a poset P=(V,=<) such that for all u,v V with u<>v, uv is an edge of G 1 if and only if there is some w V such that u=<w and v=<w and uv is an edge of G 2 if and only if there is some w V such that w=<u and w=<v. Solving two problems posed by Tanenbaum...
Following a suggestion of Tanenbaum (Electron. J. Combin. 7 (2000) R43) we introduce the notion of competition polysemic pairs of graphs. A pair of (simple) graphs (G 1 ,G 2 ) on the same set of vertices V is called competition polysemic, if there exists a digraph D=(V,A) such that for all u,v V with u<>v, uv is an edge of G 1 if and only if there is some w V such that...
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