Undirected Graphs Realizable as Graphs of Modular Lattices
1965 ◽
Vol 17
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pp. 923-932
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If (L, ≥) is a lattice or partial order we may think of its Hesse diagram as a directed graph, G, containing the single edge E(c, d) if and only if c covers d in (L, ≥). This graph we shall call the graph of (L, ≥). Strictly speaking it is the basis graph of (L, ≥) with the loops at each vertex removed; see (3, p. 170).We shall say that an undirected graph Gu can be realized as the graph of a (modular) (distributive) lattice if and only if there is some (modular) (distributive) lattice whose graph has Gu as its associated undirected graph.
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2019 ◽
Vol 28
(12)
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pp. 1950076
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1986 ◽
Vol 41
(3)
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pp. 298-303
2018 ◽
Vol 61
(4)
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pp. 848-864
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1970 ◽
Vol 13
(3)
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pp. 371-374
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2015 ◽
Vol 14
(06)
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pp. 1550088
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