New results on dually chordal graphs

PABLO DE CARIA; MARISA GUTIERREZ

Congreso; 4th Latin American Workshop on Cliques in Graphs; 2010

Universidad Federal do Rio de Janeiro

We survey some new results on dually chordal graphs, which are about eccentric vertices and new characterizations of the compatible tree in terms of minimal separators. We also study the relationship between the clique trees of a chordal graph G and the compatible trees of its clique graph K(G) and find conditions so that these trees are the same. Conversely, given a dually chordal graph H, we find all the chordal graphs G such that K(G) = H and the clique trees of G are exactly the compatible trees of H.