2 research outputs found
Graph-like Scheduling Problems and Property B
Breuer and Klivans defined a diverse class of scheduling problems in terms of
Boolean formulas with atomic clauses that are inequalities. We consider what we
call graph-like scheduling problems. These are Boolean formulas that are
conjunctions of disjunctions of atomic clauses . These problems
generalize proper coloring in graphs and hypergraphs. We focus on the existence
of a solution with all taking the value of or (i.e. problems
analogous to the bipartite case). When a graph-like scheduling problem has such
a solution, we say it has property B just as is done for -colorable
hypergraphs. We define the notion of a -uniform graph-like scheduling
problem for any integer partition . Some bounds are attained for the
size of the smallest -uniform graph-like scheduling problems without
property B. We make use of both random and constructive methods to obtain
bounds. Just as in the case of hypergraphs finding tight bounds remains an open
problem