A New Characterization of Unichord-Free Graphs

A New Characterization of Unichord-Free Graphs

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Pattern Art Unichord-free graphs are defined as having no cycle with a unique chord.They have appeared in several papers recently and are also characterized by minimal separators always inducing edgeless subgraphs (in contrast to Bandage Protectors characterizing chordal graphs by minimal separators always inducing complete subgraphs).A new characterization of unichord-free graphs corresponds to a suitable reformulation of the standard simplicial vertex characterization of chordal graphs.