Abstract   Let  H  be a bipartie graph and let  G n   be the Mycielski graph with χ( G ) =  n ,  n  ⩾ 4. Then the chromatic number of the strong product of  G   n   by  H  is at most 2 n  − 2. We use this result to show that there exist strong products of graphs in which a projection of a retract onto a factor is not a retract of the factor. We also show that in the Cartesian product of graphs  G  and  H , any tringles of  G  transfer in  H , whenever  G  and  H  are connected and  G  is strongly-triangulated, weakly-triangulated or four-cycle free.
['Sandi Klavzar']
Two remarks on retracts of graph products