Recent advances tell us that weak near unanimity (WNU) polymorphisms have an important
relationship to the CSP Dichotomoy Conjecture. In the test case of reflexive graphs, we look
the particular WNU polymorphisms known as semi-lattice (SL) polymorphisms- these have the
convenient property that they can easily be represented graphically. We look at a hierarchy of
restrictions on SL polymophisms that arises naturally as a byproduct of their graphical
representation. When we consider the classes of graphs that admit these restricted SL
polymorphisms, we find that they coincide with such well known graph classes as ‘interval’
and ‘chordal’.
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