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

Erkko Lehtonen, Jaroslav Nešetřil

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

Each clone C on a fixed base set A induces a quasi-order 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.

Original languageBritish English
Pages (from-to)1981-1995
Number of pages15
JournalEuropean Journal of Combinatorics
Volume31
Issue number8
DOIs
StatePublished - Dec 2010

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