ABSOLUTE REFLEXIVE RETRACTS AND ABSOLUTE BIPARTITE RETRACTS

It is a well-known phenomenon in the study of graph retractions that m ost results about absolute retracts in the class of bipartite (irrefle xive) graphs have analogues about absolute retracts in the class of re flexive graphs, and vice versa. In this paper we make some observation s that make the connection explicit. We develop four natural transform ations between reflexive graphs and bipartite graphs which preserve th e property of being an absolute retract, and allow us to derive result s about absolute reflexive retracts from similar results about absolut e bipartite retracts and conversely. Then we introduce generic notions that specialize to the appropriate concepts in both cases. This paves the way to a unified view of both theories, leading to absolute retra cts of general (i.e., partially reflexive) graphs.