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The classical clique tree approach to chordal graphs (and, more recently, to strongly chordal graphs) can be generalized to show a common structure for other classes of graphs, including clique graphs of chordal graphs, outerplanar graphs, distance-hereditary graphs, and chordal bipartite graphs.
Robert E. Jamison characterized chordal graphs by the edge set of every k-cycle being the symmetric difference of k-2 triangles. Strongly chordal (and chordal bipartite) graphs can be similarly characterized in terms of the distribution of triangles (respectively, quadrilaterals). These results motivate a definition of 'strongly chordal bipartite graphs', forming a class intermediate between bipartite...
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