34 research outputs found
Upper domination and upper irredundance perfect graphs
Let β(G), Γ(G) and IR(G) be the independence number, the upper domination number and the upper irredundance number, respectively. A graph G is called Γ-perfect if β(H) = Γ(H), for every induced subgraph H of G. A graph G is called IR-perfect if Γ(H) = IR(H), for every induced subgraph H of G. In this paper, we present a characterization of Γ-perfect graphs in terms of a family of forbidden induced subgraphs, and show that the class of Γ-perfect graphs is a subclass of IR-perfect graphs and that the class of absorbantly perfect graphs is a subclass of Γ-perfect graphs. These results imply a number of known theorems on Γ-perfect graphs and IR-perfect graphs. Moreover, we prove a sufficient condition for a graph to be Γ-perfect and IR-perfect which improves a known analogous result. © 1998 Elsevier Science B.V. All rights reserved
Нахождение областей сходимости и вычисление сумм степенных рядов от h-комплексного переменного
Herein, taking power series from a real variable that converge on a certain interval to known sums, the authors consider the power series with the same coefficients from an h-complex variable. For such series, the interiors of the regions of convergence are found, and their sums are explicitly expressed in terms of the sums of the original series. Along the way, the problem of isolation conditions for the zeros of the sums of such series is solved.Взяв степенные ряды от вещественного переменного, сходящиеся на некотором интервале к известным суммам, авторы рассматривают степенные ряды с теми же коэффициентами от h-комплексного переменного. Для таких рядов найдены внутренности областей сходимости, а их суммы явно выражены через суммы исходных рядов. Попутно решен вопрос об условиях изолированности нулей сумм таких рядов
The nonabelian Liouville-Arnold integrability by quadratures problem: a symplectic approach
A symplectic theory approach is devised for solving the problem of
algebraic-analytical construction of integral submanifold imbeddings for
integrable (via the nonabelian Liouville-Arnold theorem) Hamiltonian systems on
canonically symplectic phase spaces
Physically Realistic Solutions to the Ernst Equation on Hyperelliptic Riemann Surfaces
We show that the class of hyperelliptic solutions to the Ernst equation (the
stationary axisymmetric Einstein equations in vacuum) previously discovered by
Korotkin and Neugebauer and Meinel can be derived via Riemann-Hilbert
techniques. The present paper extends the discussion of the physical properties
of these solutions that was begun in a Physical Review Letter, and supplies
complete proofs. We identify a physically interesting subclass where the Ernst
potential is everywhere regular except at a closed surface which might be
identified with the surface of a body of revolution. The corresponding
spacetimes are asymptotically flat and equatorially symmetric. This suggests
that they could describe the exterior of an isolated body, for instance a
relativistic star or a galaxy. Within this class, one has the freedom to
specify a real function and a set of complex parameters which can possibly be
used to solve certain boundary value problems for the Ernst equation. The
solutions can have ergoregions, a Minkowskian limit and an ultrarelativistic
limit where the metric approaches the extreme Kerr solution. We give explicit
formulae for the potential on the axis and in the equatorial plane where the
expressions simplify. Special attention is paid to the simplest non-static
solutions (which are of genus two) to which the rigidly rotating dust disk
belongs.Comment: 32 pages, 2 figures, uses pstricks.sty, updated version (October 7,
1998), to appear in Phys. Rev.
Large-scale optimization with the primal-dual column generation method
The primal-dual column generation method (PDCGM) is a general-purpose column
generation technique that relies on the primal-dual interior point method to
solve the restricted master problems. The use of this interior point method
variant allows to obtain suboptimal and well-centered dual solutions which
naturally stabilizes the column generation. As recently presented in the
literature, reductions in the number of calls to the oracle and in the CPU
times are typically observed when compared to the standard column generation,
which relies on extreme optimal dual solutions. However, these results are
based on relatively small problems obtained from linear relaxations of
combinatorial applications. In this paper, we investigate the behaviour of the
PDCGM in a broader context, namely when solving large-scale convex optimization
problems. We have selected applications that arise in important real-life
contexts such as data analysis (multiple kernel learning problem),
decision-making under uncertainty (two-stage stochastic programming problems)
and telecommunication and transportation networks (multicommodity network flow
problem). In the numerical experiments, we use publicly available benchmark
instances to compare the performance of the PDCGM against recent results for
different methods presented in the literature, which were the best available
results to date. The analysis of these results suggests that the PDCGM offers
an attractive alternative over specialized methods since it remains competitive
in terms of number of iterations and CPU times even for large-scale
optimization problems.Comment: 28 pages, 1 figure, minor revision, scaled CPU time
Contributions to the theory of graphic sequences
In this article we present a new version of the Erdős-Gallai theorem concerning graphicness of the degree sequences. The best conditions of all known on the reduction of the number of Erdős-Gallai inequalities are given. Moreover, we prove a criterion of the bipartite graphicness and give a sufficient condition for a sequence to be graphic which does not require checking of any Erdős-Gallai inequality. © 1992
Disproof of a Conjecture in the Domination Theory
In [1] C. Barefoot, F. Harary and K. Jones conjectured that for cubic graphs with connectivity three the difference between the domination and independent domination numbers is at most one. We disprove this conjecture and give an exhaustive answer to the question: “What is the difference between the domination and independent domination numbers for cubic graphs with given connectivity?” © 1994, Springer-Verlag. All rights reserved
Perfect graphs of strong domination and independent strong domination
AbstractLet γ(G), i(G), γS(G) and iS(G) denote the domination number, the independent domination number, the strong domination number and the independent strong domination number of a graph G, respectively. A graph G is called γi-perfect (domination perfect) if γ(H)=i(H), for every induced subgraph H of G. The classes of γγS-perfect, γSiS-perfect, iiS-perfect and γiS-perfect graphs are defined analogously. In this paper we present a number of characterization results on the above classes of graphs. For example, characterizations of K4-free γSiS-perfect graphs and triangle-free γiS-perfect graphs are given. Moreover, the strong dominating set and independent strong dominating set problems as well as the weak dominating set and independent weak dominating set problems are shown to be NP-complete on a class of graphs. Several problems and conjectures are proposed