Characterizing subclasses of cover-incomparability graphs by forbidden subposets
Abstract
In this paper we continue investigations of cover-incomparability graphs of finite partially ordered sets (see Bres,Bres2,Bres3,Bres4 and Max,MaxDH). We consider in some detail the distinction between cover-preserving subsets and isometric subsets of a partially ordered set. This is critical to understanding why forbidden subposet characterizations of certain classes of cover-incomparability graphs in Bres and Bres3 are not valid as presented. Here we provide examples, investigate the root of the difficulties, and formulate and prove valid revisions of these characterizations.
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