Computation of the Interval Order Dimension Sample Clauses

Computation of the Interval Order Dimension. If C is a chain subgraph of G(H), also its bipartite complement is a chain graph (as the bipartite complement of a 2K2 is a 2K2), so we have that Idim(H) coincides with the size of a minimum chain subgraph cover of the bipartite complement of G(H). All this is contained in the following result of [91] where by abuse of notation the bipartite complement of G(H) is denoted by B(H) (instead of B(G(H))) and the size of a minimum chain subgraph cover of B(H) is denoted by ch(B(H)): Proposition 7 ([91]). Let H be a bipartite poset. Then Idim(H)= ch(B(H)). From this we have a straightforward interpretation of our results on the computation of the size of a minimum chain subgraph cover (see Theorem 4):
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