We study the Lovász-Schrijver SDP-operator applied to the fractional stable set polytope of graphs. The problem of obtaining a combinatorial characterization of graphs for which the SDP-operator generates the stable set polytope in one step has been open since 1990. In an earlier publication, we named these graphs N+-perfect. In the current contribution, we propose a conjecture on combinatorial...

In this paper, we analyze the strength of split cuts in a lift-and-project framework. We first observe that the Lovász-Schrijver and Sherali-Adams lift-and-project operator hierarchies can be viewed as applying specific 0-1 split cuts to an appropriate extended formulation and demonstrate how to strengthen these hierarchies using additional split cuts. More precisely, we define a new operator t...

In this paper, we consider symmetric jump processes of mixed-type on metric measure spaces under general volume doubling condition, and establish stability of two-sided heat kernel estimates and heat kernel upper bounds. We obtain their stable equivalent characterizations in terms of the jumping kernels, modifications of cut-off Sobolev inequalities, and the Faber-Krahn inequalities. In particu...

The Loebl–Komlós–Sós conjecture states that for any integers k and n, if a graph G on n vertices has at least n/2 vertices of degree at least k, then G contains as subgraphs all trees on k + 1 vertices. We prove this conjecture in the case when k is linear in n, and n is sufficiently large. © 2009 Elsevier B.V. All rights reserved.

The Erdős-Faber-Lovász conjecture is the statement that every graph that is the union of n cliques of size n intersecting pairwise in at most one vertex has chromatic number n. Kahn and Seymour proved a fractional version of this conjecture, where the chromatic number is replaced by the fractional chromatic number. In this note we investigate similar fractional relaxations of the Erdős-Faber-Lo...

The Maier-Saupe theory is employed in order to calculate order parameters (P 2 ) , (P4) f rom the nematic potential q. The relation between <r=q/(RT) and S = (P2) corresponds well with a recently established formula by Kalmykov. The relation between the order parameters is in accordance with the analytic expression (P4)=5/l (P2) proposed by Zanonni, but deviates significantly f rom the Faber mo...

We prove a comparison theorem of Faber-Krahn type and a sharp bound for the compact surfaces with negative Euler characteristic via the Ricci flow.

It is shown in a previous work that Faber-Pandharipande-Zagier's and Miki's identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions. Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series ...

The main goal of the present paper is to construct some families of the Carlitz's $q$-Bernoulli polynomials and numbers. We firstly introduce the modified Carlitz's $q$-Bernoulli polynomials and numbers with weight ($_{p}$. We then define the modified degenerate Carlitz's $q$-Bernoulli polynomials and numbers with weight ($alpha ,beta $) and obtain some recurrence relations and other identities...