Retracts of products of chordal graphsBrešar, Boštjan (Avtor) Chalopin, Jérémie (Avtor) Chepoi, Victor (Avtor) Kovše, Matjaž (Avtor) Labourel, Arnaud (Avtor) Vaxès, Yann (Avtor) teorija grafovgrafretraktzastražena amalgamacijatetiven grafkartezični produkt grafovmedianski grafgraph theorygraphretractgated amalgamationchordal graphCartesian product of graphsmedian graphWe characterize the graphs ▫$G$▫ that are retracts of Cartesian products of chordal graphs. We show that they are exactly the weakly modular graphs that do not contain ▫$K_{2;3}$▫, ▫$k$▫-wheels ▫$W_k$▫, and ▫$k$▫-wheels minus one spoke T$W_k^- ; (k ge 4)$T as induced subgraphs. We also show that these graphs ▫$G$▫ are exactly the cage-amalgamation graphs introduced by Brešar and Tepeh Horvat (2009); this solves the open question raised by these authors. Finally, we prove that replacing all products of cliques of $G$ by products of "solid" simplices, we obtain a polyhedral cell complex which, endowed with an intrinsic Euclidean metric, is a CAT(0) space. This generalizes similar results about median graphs as retracts of hypercubes (products of edges) and median graphs as 1-skeletons of CAT(0) cubical complexes.20102015-07-10 15:18:18Delo ni kategorizirano51873sl