90 research outputs found
Translating Concepts of State Transfer to Spin-1 Chains
State transfer is a well-known routine for various systems of
spins-. Still, it is not well studied for chains of spins of larger
magnitudes. In this contribution we argue that while perfect state transfer may
seem unnatural in spin-1 systems, it is still feasible for arrays of V-type
three-level atoms. Tomography of such 1D array is also shown to be possible by
acting on one atom from such an array
-set problem in graphs
A subset of a graph is a -set if every
vertex is adjacent to at least but not more than
vertices in D. The cardinality of a minimum -set of , denoted as
, is called the -domination number of . Given a
graph and an integer , the decision version of the -set
problem is to decide whether has a -set of cardinality at most .
In this paper, we first obtain an upper bound on using
probabilistic methods, for bounded minimum and maximum degree graphs. Our bound
is constructive, by the randomized algorithm of Moser and Tardos [MT10], We
also show that the - set problem is NP-complete for chordal graphs.
Finally, we design two algorithms for finding of a tree
and a split graph, for any fixed , which answers an open question posed in
[CHHM13]
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