Related papers: Stable Sets and Graphs with no Even Holes

To compute solutions of sparse polynomial systems efficiently we have to exploit the structure of their Newton polytopes. While the application of polyhedral methods naturally excludes solutions with zero components, an irreducible…

In this paper we extend three results about polycycles (also known as graphs) of planar smooth vector field to planar non-smooth vector fields (also known as piecewise vector fields, or Filippov systems). The polycycles considered here may…

In this paper we show that graphs of "neighbourly" cubical complexes -- cubical complexes in which every pair of vertices spans a (unique) cube -- have good expansion properties, using a technique based on multicommodity flows. By showing…

In this paper, we study the ideas of composition and decomposition in the context of vector spaces, graphs and matroids. For vector spaces $\V_{AB},$ treated as collection of row vectors, with specified column set $A\uplus B,$ we define…

An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements for various sets of polynomial bases. For the maximal order bases, a new set of correction…

In this paper, the stability of fractional differential equations (FDEs) with unknown parameters is studied. FDEs bring many advantages to model the physical systems in the nature or man-made systems in the industry. Because this…

In this article we use the combinatorial and geometric structure of manifolds with embedded cylinders in order to develop an adiabatic decomposition of the Hodge cohomology of these manifolds. We will on the one hand describe the adiabatic…

This paper is devoted to the convergence and stability analysis of a class of nonlinear subdivision schemes and associated multi-resolution transforms. These schemes are defined as a perturbation of a linear subdivision scheme. Assuming a…

Functional digraphs are unlabelled finite digraphs where each vertex has exactly one out-neighbor. They are isomorphic classes of finite discrete-time dynamical systems. Endowed with the direct sum and product, functional digraphs form a…

A three-path-configuration is a graph consisting of three pairwise internally-disjoint paths the union of every two of which is an induced cycle of length at least four. A graph is 3PC-free if no induced subgraph of it is a…

We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…

The aim of this paper is to extend and generalise some work of Katona on the existence of perfect matchings or Hamilton cycles in graphs subject to certain constraints. The most general form of these constraints is that we are given a…

We study the perfect matching reconfiguration problem: Given two perfect matchings of a graph, is there a sequence of flip operations that transforms one into the other? Here, a flip operation exchanges the edges in an alternating cycle of…

Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…

De Berg et al. in [SICOMP 2020] gave an algorithmic framework for subexponential algorithms on geometric graphs with tight (up to ETH) running times. This framework is based on dynamic programming on graphs of weighted treewidth resulting…

High-order ARX models can be used to approximate a quite general class of linear systems in a parametric model structure, and well-established methods can then be used to retrieve the true plant and noise models from the ARX polynomials.…

We show that the Maximum Weight Independent Set problem (MWIS) can be solved in quasi-polynomial time on $H$-free graphs (graphs excluding a fixed graph $H$ as an induced subgraph) for every $H$ whose every connected component is a path or…

We introduce a new compactification of the space of relative stable maps. This new method uses logarithmic geoemtry in the sense of Kato-Fontaine-Illusie rather than the expanded degeneration. The underlying structure of our log stable maps…

Let G=(V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v in V dominates its closed neighborhood N[v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v in V, there is…

In this document, we deal with the stabilization problem of slow-fast systems (or singularly perturbed Ordinary Differential Equations) at a non-hyperbolic point. The class of systems studied here have the following properties: 1) they have…