16 research outputs found
Pseudorandom hypergraph matchings
A celebrated theorem of Pippenger states that any almost regular hypergraph
with small codegrees has an almost perfect matching. We show that one can find
such an almost perfect matching which is `pseudorandom', meaning that, for
instance, the matching contains as many edges from a given set of edges as
predicted by a heuristic argument.Comment: 14 page
Non-monotone target sets for threshold values restricted to , , and the vertex degree
We consider a non-monotone activation process
on a graph , where , for every positive integer , and is a threshold function. The set is a so-called non-monotone
target set for if there is some such that for every
. Ben-Zwi, Hermelin, Lokshtanov, and Newman [Discrete Optimization 8
(2011) 87-96] asked whether a target set of minimum order can be determined
efficiently if is a tree. We answer their question in the affirmative for
threshold functions satisfying for every
vertex~. For such restricted threshold functions, we give a characterization
of target sets that allows to show that the minimum target set problem remains
NP-hard for planar graphs of maximum degree but is efficiently solvable for
graphs of bounded treewidth