Independent domination in hereditary classes

AbstractWe investigate Independent Domination Problem within hereditary classes of graphs. Boliac and Lozin [Independent domination in finitely defined classes of graphs, Theoret. Comput. Sci. 301 (1–3) (2003) 271–284] proved some sufficient conditions for Independent Domination Problem to be NP-complete within finitely defined hereditary classes of graphs. They posed a question whether the conditions are also necessary. We show that the conditions are not necessary, since Independent Domination Problem is NP-hard within 2P3-free graphs.Moreover, we show that the problem remains NP-hard for a new hereditary class of graphs, called hereditary 3-satgraphs. We characterize hereditary 3-satgraphs in terms of forbidden induced subgraph. As corollaries, we prove that Independent Domination Problem is NP-hard within the class of all 2P3-free perfect graphs and for K1,5-free weakly chordal graphs.Finally, we compare complexity of Independent Domination Problem with that of Independent Set Problem for a hierarchy of hereditary classes recently proposed by Hammer and Zverovich [Construction of maximal stable sets with k-extensions, Combin. Probab. Comput. 13 (2004) 1–8]. For each class in the hierarchy, a maximum independent set can be found in polynomial time, and the hierarchy covers all graphs. However, our characterization of hereditary 3-satgraphs implies that Independent Domination Problem is NP-hard for almost all classes in the hierarchy. This fact supports a conjecture that Independent Domination is harder than Independent Set Problem within hereditary classes

Minimal Models of CFT on Z_N-Surfaces

The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.Comment: 16 pages, latex, no figures; two important early references on the coset construction have been included; to appear in Mod. Phys. Let

Algorithm of global uniformization of algebraic correspondence

The problem of global uniformization of algebraic correspondence is investigated. The weaker assumptions are used in the analysis. First Published Online: 14 Oct 201

ДВА ОБОБЩЕНИЯ ПОЛИГАММА-ФУНКЦИЙ

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АЛГОРИТМ ПОСТРОЕНИЯ КОНФОРМНОГО ГОМЕОМОРФИЗМА КОНЕЧНОЛИСТНОЙ РИМАНОВОЙ ПОВЕРХНОСТИ НА ПЛОСКОСТЬ

We consider a finite-sheeted covering surface of the sphere of genus zero. We built the algorithm of construction of the conformal homeomorphism of this surface on the sphere by a given branch point and permutations describing the sheets gluing order. Рассматривается конечнолистная рода нуль поверхность наложения сферы. Дается алгоритм построения конформного гомеоморфизма этой поверхности на сферу по заданным точкам разветвления и подстановкам, описывающим закон склеивания листов.

ОБОБЩЕНИЕ ФОРМУЛЫ ПЕРЕСТАНОВКИ ПУАНКАРЕ БЕРТРАНА

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Вычисление гармонических мер компонент края конечносвязной области

The article proposes a new method for calculating harmonic measures of the boundary components of the finitely connected domain.В статье предложен новый способ вычисления гармонических мер компонент края конечносвязной области

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

Решение интегро-дифференциальных уравнений с сингулярными и гиперсингулярными интегралами специального вида

Quadrature linear integro-differential equations on a closed curve located in the complex plane are solved. The equations contain singular integrals which are understood in the sense of the main value and hypersingular integrals which are understood in the sense of the Hadamard finite part. The coefficients of the equations have a special structure.Приведены в явном виде решения линейных интегро-дифференциальных уравнений. Уравнения решаются на замкнутой кривой, принадлежащей комплексной плоскости. Коэффициенты уравнений имеют специальный вид. Интегралы в уравнениях понимаются в смысле главного значения и в смысле конечной части по Адамару

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.