10,874 research outputs found
Spanning Eulerian subgraphs and Catlin’s reduced graphs
A graph G is collapsible if for every even subset R ⊆ V (G), there is a spanning connected subgraph HR of G whose set of odd degree vertices is R. A graph is reduced if it has no nontrivial collapsible subgraphs. Catlin [4] showed that the existence of spanning Eulerian subgraphs in a graph G can be determined by the reduced graph obtained from G by contracting all the collapsible subgraphs of G. In this paper, we present a result on 3-edge-connected reduced graphs of small orders. Then, we prove that a 3-edge-connected graph G of order n either has a spanning Eulerian subgraph or can be contracted to the Petersen graph if G satisfies one of the following:
(i) d(u) + d(v) \u3e 2(n/15 − 1) for any uv 6∈ E(G) and n is large;
(ii) the size of a maximum matching in G is at most 6;
(iii) the independence number of G is at most 5.
These are improvements of prior results in [16], [18], [24] and [25]
The second order nonlinear conductance of a two-dimensional mesoscopic conductor
We have investigated the weakly non-linear quantum transport properties of a
two-dimensional quantum conductor. We have developed a numerical scheme which
is very general for this purpose. The nonlinear conductance is computed by
explicitly evaluating the various partial density of states, the sensitivity
and the characteristic potential. Interesting spatial structure of these
quantities are revealed. We present detailed results concerning the crossover
behavior of the second order nonlinear conductance when the conductor changes
from geometrically symmetrical to asymmetrical. Other issues of interests such
as the gauge invariance are also discussed.Comment: LaTe
Quantum Brownian motion model for the stock market
It is believed by the majority today that the efficient market hypothesis is
imperfect because of market irrationality. Using the physical concepts and
mathematical structures of quantum mechanics, we construct an econophysics
framework for the stock market, based on which we analogously map massive
numbers of single stocks into a reservoir consisting of many quantum harmonic
oscillators and their stock index into a typical quantum open system--a quantum
Brownian particle. In particular, the irrationality of stock transactions is
quantitatively considered as the Planck constant within Heisenberg's
uncertainty relationship of quantum mechanics in an analogous manner. We
analyze real stock data of Shanghai Stock Exchange of China and investigate
fat-tail phenomena and non-Markovian behaviors of the stock index with the
assistance of the quantum Brownian motion model, thereby interpreting and
studying the limitations of the classical Brownian motion model for the
efficient market hypothesis from a new perspective of quantum open system
dynamics
Properties of Catlin's reduced graphs and supereulerian graphs
A graph is called collapsible if for every even subset ,
there is a spanning connected subgraph of such that is the set of
vertices of odd degree in . A graph is the reduction of if it is
obtained from by contracting all the nontrivial collapsible subgraphs. A
graph is reduced if it has no nontrivial collapsible subgraphs. In this paper,
we first prove a few results on the properties of reduced graphs. As an
application, for 3-edge-connected graphs of order with for any where are given, we show how such graphs
change if they have no spanning Eulerian subgraphs when is increased from
to 10 then to
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