Delne kocke so razdaljni grafi

Chatrand, Kubicki in Schultz [Aequationes Math. 55 (1998) 129-145] so postavili domnevo, da so vsi dvodelni grafi razdaljni grafi. V tem članku pokažemo, da so vsi grafi podmnožice dvodelnih grafov, in sicer delne kocke, razdaljni grafi.Chatrand, Kubicki and Schultz [Aequationes Math. 55 (1998) 129-145] have recently conjectured that all bipartite graphs are distance graphs. Here we show that all graphs of a large subclass of bipartite graphs, i.e. partial cubes, are distance graphs