Abstract
In this paper the authors establish a one-to-one correspondence between the isomorphism classes of graphs whose structure spaces are r-regular partial planes and the isomorphism classes of graphs which have no induced subgraphs isomorphic to an ( r + 1)-pointed star or to K 4 with a single line removed. Moreover the graphs whose structure space contains no 4-loops correspond to graphs with no 4-cycles as induced subgraphs. It is pointed out that these graphs give rise to orthomodular posets (or lattices in the case of no 4-loops) and hence are of much interest in the study of orthomodular structures and in particular of quantum logics.
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