Minors of Boolean functions with respect to clique functions and hypergraph homomorphisms

Each clone C on a fixed base set A determines a quasiorder on the set of all operations on A by the following rule: f is a C-minor of g if f can be obtained by substituting operations from C for the variables of g. By making use of a representation of Boolean functions by hypergraphs and hypergraph homomorphisms, it is shown that a clone C on {0, 1} has the property that the corresponding C-minor partial order is universal if and only if C is one of the countably many clones of clique functions or the clone of self-dual monotone functions. Furthermore, the C-minor partial orders are dense when C is a clone of clique functions.

• Type: Journal
• Year: 2010
• Where: EJC
• Authors: Erkko Lehtonen, Jaroslav Nesetril
• Keywords: C-minor Partial Orders, Clique Functions, EJC 2007, EJC 2010, Fixed Base