Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on n vertices with maximum degree 3 is at most 1 3 n + 2. We disprove this conjecture by constructing a collection of connected graphs {Gn} with maximum degree 3 on arbitrarily large number of vertices, having zero forcing number at least 4 9 |Gn|.

Zero forcing is a combinatorial game played on a graph with a goal of changing the color of every vertex at minimal cost. This leads to a parameter known as the zero forcing number that can be used to give an upper bound for the maximum nullity of a matrix associated with the graph. A variation on the zero forcing game is introduced that can be used to give an upper bound for the maximum nullit...

We give characterizations for the (in ZFC unprovable) sentences “Every Σ12–set is measurable” and “Every ∆ 1 2–set is measurable” for various notions of measurability derived from well–known forcing partial orderings.

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

By the technique of forcing, some new independence results are proved for the alternative set theory (AST) and similar weak theories: The scheme of choice is independent both of AST and of second order arithmetic, axiom of constructibility is independent of AST plus schemes of choice.

In this paper we consider MIMO broadcast channels with separable variance profile modelling antenna correlation at both transmit and receive sides. For large number of antennas we derive the theoretical sum-rate capacity when the transmitter performs zero-forcing or regularized zero-forcing precoding. In particular, we apply the results to volumelimited devices where the correlation originates ...

traditional work on pro-drop languages identified a set of parametric values ‎associated with the availability of null subjects, including the presence of null ‎expletive subjects. in the same vein, but more within the framework of minimalist ‎program, i will discuss while referential subjects may optionally be overt or covert ‎in the persian, expletives are obligatorily null. in this regard, a...