179,099 research outputs found
Cyclically five-connected cubic graphs
A cubic graph is cyclically 5-connected if is simple, 3-connected,
has at least 10 vertices and for every set of edges of size at most four,
at most one component of contains circuits. We prove that if
and are cyclically 5-connected cubic graphs and topologically
contains , then either and are isomorphic, or (modulo well-described
exceptions) there exists a cyclically 5-connected cubic graph such that
topologically contains and is obtained from in one of the
following two ways. Either is obtained from by subdividing two
distinct edges of and joining the two new vertices by an edge, or is
obtained from by subdividing each edge of a circuit of length five and
joining the new vertices by a matching to a new circuit of length five disjoint
from in such a way that the cyclic orders of the two circuits agree. We
prove a companion result, where by slightly increasing the connectivity of
we are able to eliminate the second construction. We also prove versions of
both of these results when is almost cyclically 5-connected in the sense
that it satisfies the definition except for 4-edge cuts such that one side is a
circuit of length four. In this case is required to be almost cyclically
5-connected and to have fewer circuits of length four than . In particular,
if has at most one circuit of length four, then is required to be
cyclically 5-connected. However, in this more general setting the operations
describing the possible graphs are more complicated.Comment: 47 pages, 5 figures. Revised according to referee's comments. To
appear in J. Combin. Theory Ser.
K-6 minors in large 6-connected graphs
Jorgensen conjectured that every 6-connected graph with no K-6 minor has a vertex whose deletion makes the graph planar. We prove the conjecture for all sufficiently large graphs. (C) 2017 Published by Elsevier Inc
Declarative Specification
Deriving formal specifications from informal requirements is extremely difficult since one has to overcome the conceptual gap between an application domain and the domain of formal specification methods. To reduce this gap we introduce application-specific specification languages, i.e., graphical and textual notations that can be unambiguously mapped to formal specifications in a logic language. We describe a number of realised approaches based on this idea, and evaluate them with respect to their domain specificity vs. generalit
Assessing Homeowner Risk and Knowledge in Mitigating Nonpoint Source Pollution in Coastal Watersheds
Boundary operator algebras for free uniform tree lattices
Let be a finite connected graph, each of whose vertices has degree at
least three. The fundamental group of is a free group and acts on
the universal covering tree and on its boundary ,
endowed with a natural topology and Borel measure. The crossed product
-algebra depends only on the rank of
and is a Cuntz-Krieger algebra whose structure is explicitly
determined. The crossed product von Neumann algebra does not possess this
rigidity. If is homogeneous of degree then the von Neumann algebra
is the hyperfinite factor of type
where if is bipartite, and
otherwise
Euro-Ibero American Seminar: Cooperation on Drugs and Drug Addiction Policies. Conference proceedings. Oporto, Portugal, 8-9 October 1998
An Expanding Locally Anisotropic (ELA) Metric Describing Matter in an Expanding Universe
It is suggested an expanding locally anisotropic metric (ELA) ansatz
describing matter in a flat expanding universe which interpolates between the
Schwarzschild (SC) metric near point-like central bodies of mass 'M' and the
Robertson-Walker (RW) metric for large radial coordinate: 'ds^2=Z(cdt)2 - 1/Z
(dr1-(Hr1/c) Z^(alpha/2+1/2)(cdt))^2-r1^2 dOmega', where 'Z=1-U' with
'U=2GM/(c^2r1)', 'G' is the Newton constant, 'c' is the speed of light,
'H=H(t)=\dot(a)/a' is the time-dependent Hubble rate,
'dOmega=dtheta^2+sin^2(theta) dvarphi^2' is the solid angle element, 'a' is the
universe scale factor and we are employing the coordinates 'r1=ar', being 'r'
the radial coordinate for which the RW metric is diagonal. For constant
exponent 'alpha=alpha0=0' it is retrieved the isotropic McVittie (McV) metric
and for 'alpha=alpha0=1' it is retrieved the locally anisotropic
Cosmological-Schwarzschild (SCS) metric, both already discussed in the
literature. However it is shown that only for constant exponent 'alpha=alpha0>
1' exists an event horizon at the SC radius 'r1=2GM/c^2' and only for
'alpha=alpha0>= 3' space-time is singularity free for this value of the radius.
These bounds exclude the previous existing metrics, for which the SC radius is
a naked extended singularity. In addition it is shown that for 'alpha=alpha0>5'
space-time is approximately Ricci flat in a neighborhood of the event horizon
such that the SC metric is a good approximation in this neighborhood. It is
further shown that to strictly maintain the SC mass pole at the origin 'r1=0'
without the presence of more severe singularities it is required a radial
coordinate dependent correction to the exponent 'alpha(r1)=alpha0+alpha1
'2GM/(c^2 r1)' with a negative coefficient 'alpha1<0'. The energy-momentum
density, pressures and equation of state are discussed.Comment: 6 pages; 2 figures; covers some of the derivations in arXiv:0907.0847
with corrected terminology and a new discussion of the event horizon
- …