2Complexes, (hyper)graphs, and inequality systems
In many problems of combinatorial optimization, it is necessary to distinguish in an abstract simplicial complex its facet or a collection of facets with some properties, say of maximal dimension. Recall that in our study complexes often serve as combinatorial models of (in)feasible monotone systems of constraints – the multi-indices (or the constructions marked with them) of feasible subsystems represent the faces of complexes. Thus, a complex with a unique facet corresponds to a feasible system, and a complex with several facets emulates an infeasible system. In this context, it is interesting to investigate the structural properties of the facet family of a complex and, in particular, to investigate ...
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