%0 Journal Article %T A variant of the bipartite relation theorem and its application to clique graphs %A Kazuhiro Kawamura %J Contributions to Discrete Mathematics %D 2011 %I University of Calgary %X We consider a homological variant of the Bipartite Relation Theorem (cite{bjorner}) in the context of the flag complex of the square of a bipartite graph (cite{lpvf}). We apply the results to study the homology and homotopy groups of the flag complexes of clique graphs. %U http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/241