37,520 research outputs found
Tight upper bound on the maximum anti-forcing numbers of graphs
Let be a simple graph with a perfect matching. Deng and Zhang showed that
the maximum anti-forcing number of is no more than the cyclomatic number.
In this paper, we get a novel upper bound on the maximum anti-forcing number of
and investigate the extremal graphs. If has a perfect matching
whose anti-forcing number attains this upper bound, then we say is an
extremal graph and is a nice perfect matching. We obtain an equivalent
condition for the nice perfect matchings of and establish a one-to-one
correspondence between the nice perfect matchings and the edge-involutions of
, which are the automorphisms of order two such that and
are adjacent for every vertex . We demonstrate that all extremal
graphs can be constructed from by implementing two expansion operations,
and is extremal if and only if one factor in a Cartesian decomposition of
is extremal. As examples, we have that all perfect matchings of the
complete graph and the complete bipartite graph are nice.
Also we show that the hypercube , the folded hypercube ()
and the enhanced hypercube () have exactly ,
and nice perfect matchings respectively.Comment: 15 pages, 7 figure
The maximum forcing number of polyomino
The forcing number of a perfect matching of a graph is the
cardinality of the smallest subset of that is contained in no other perfect
matchings of . For a planar embedding of a 2-connected bipartite planar
graph which has a perfect matching, the concept of Clar number of hexagonal
system had been extended by Abeledo and Atkinson as follows: a spanning
subgraph of is called a Clar cover of if each of its components is
either an even face or an edge, the maximum number of even faces in Clar covers
of is called Clar number of , and the Clar cover with the maximum number
of even faces is called the maximum Clar cover. It was proved that if is a
hexagonal system with a perfect matching and is a set of hexagons in a
maximum Clar cover of , then has a unique 1-factor. Using this
result, Xu {\it et. at.} proved that the maximum forcing number of the
elementary hexagonal system are equal to their Clar numbers, and then the
maximum forcing number of the elementary hexagonal system can be computed in
polynomial time. In this paper, we show that an elementary polyomino has a
unique perfect matching when removing the set of tetragons from its maximum
Clar cover. Thus the maximum forcing number of elementary polyomino equals to
its Clar number and can be computed in polynomial time. Also, we have extended
our result to the non-elementary polyomino and hexagonal system
Six Noise Type Military Sound Classifier
Blast noise from military installations often has a negative impact on the quality of life of residents living in nearby communities. This negatively impacts the military's testing \& training capabilities due to restrictions, curfews, or range closures enacted to address noise complaints. In order to more directly manage noise around military installations, accurate noise monitoring has become a necessity. Although most noise monitors are simple sound level meters, more recent ones are capable of discerning blasts from ambient noise with some success. Investigators at the University of Pittsburgh previously developed a more advanced noise classifier that can discern between wind, aircraft, and blast noise, while simultaneously lowering the measurement threshold. Recent work will be presented from the development of a more advanced classifier that identifies additional classes of noise such as machine gun fire, vehicles, and thunder. Additional signal metrics were explored given the increased complexity of the classifier. By broadening the types of noise the system can accurately classify and increasing the number of metrics, a new system was developed with increased blast noise accuracy, decreased number of missed events, and significantly fewer false positives
On the Computational Complexity of Defining Sets
Suppose we have a family of sets. For every , a
set is a {\sf defining set} for if is the
only element of that contains as a subset. This concept has been
studied in numerous cases, such as vertex colorings, perfect matchings,
dominating sets, block designs, geodetics, orientations, and Latin squares.
In this paper, first, we propose the concept of a defining set of a logical
formula, and we prove that the computational complexity of such a problem is
-complete.
We also show that the computational complexity of the following problem about
the defining set of vertex colorings of graphs is -complete:
{\sc Instance:} A graph with a vertex coloring and an integer .
{\sc Question:} If be the set of all -colorings of
, then does have a defining set of size at most ?
Moreover, we study the computational complexity of some other variants of
this problem
Heavy Quarks: Lessons Learned from HERA and Tevatron
We review some of the recent developments which have enabled the heavy quark
mass to be incorporated into both the calculation of the hard-scattering cross
section and the PDFs. We compare and contrast some of the schemes that have
been used in recent global PDF analyses, and look at issues that arise when
these calculations are extended to NNLO.Comment: 11 pages, 9 figures, to appear in the proceedings of the Ringberg
Workshop "New Trends in HERA Physics 2008
- …