Related papers: Strongly regular configurations
We study the structure of the asymptotic expansion of the probability that a combinatorial object is connected. We show that the coefficients appearing in those asymptotics are integers and can be interpreted as the counting sequences of…
We give a combinatorial characterization of graphs whose normalized Laplacian has three distinct eigenvalues. Strongly regular graphs and complete bipartite graphs are examples of such graphs, but we also construct more exotic families of…
It is proved that the numerical semigroups associated to the combinatorial configurations satisfy a family of non-linear symmetric patterns. Also, these numerical semigroups are studied for two particular classes of combinatorial…
Twelve new strongly regular graphs with parameters (81,30,9,12) are found as graphs invariant under certain subgroups of the automorphism groups of the two previously known graphs that arise from 2-weight codes. One of these new graphs is…
Higher-dimensional orthogonal packing problems have a wide range of practical applications, including packing, cutting, and scheduling. Previous efforts for exact algorithms have been unable to avoid structural problems that appear for…
In this paper, we study combinatorial properties of stable curves. To the dual graph of any nodal curve, it is naturally associated a group, which is the group of components of the N\'eron model of the generalized Jacobian of the curve. We…
Necessary and sufficient conditions are obtained for the infinitesimal rigidity of braced grids in the plane with respect to non-Euclidean norms. Component rectangles of the grid may carry 0, 1 or 2 diagonal braces, and the combinatorial…
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings. Beside the study of a specific graph…
Understanding which system structure can sustain stable dynamics is a fundamental step in the design and analysis of large scale dynamical systems. Towards this goal, we investigate here the structural stability of systems with a random…
We provide a way of determining the infinitesimal rigidity of rod configurations realizing a rank two incidence geometry in the Euclidean plane. We model each rod with a cone over its point set and prove that the resulting geometric…
In this paper we consider the question of when a strongly regular graph with parameters $((s+1)(st+1),s(t+1),s-1,t+1)$ can exist. These parameters arise when the graph is derived from a generalized quadrangle, but there are other examples…
In the present note we study some arrangements of inflectional lines, hyperosculating conics, and a nodal plane cubic that are free. Moreover, we study weak combinatorics of arrangements consisting of lines, conics, and elliptic curves…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
We investigate the second smallest unresolved feasible set of parameters of strongly regular graphs, $(v,k,\lambda,\mu)=(85,14,3,2)$. Using the classification of cubic graphs of small degree, we restrict possible local structure of such a…
We will look for stable structures in four situations and discuss what is known and unknown.
We consider partially ordered sets of combinatorial structures under consecutive orders, meaning that two structures are related when one embeds in the other such that `consecutive' elements remain consecutive in the image. Given such a…
We exhibit a new construction of edge-regular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this construction includes an edge-regular graph with parameters $(24,8,2)$. We also show…
Highly connected and yet sparse graphs (such as expanders or graphs of high treewidth) are fundamental, widely applicable and extensively studied combinatorial objects. We initiate the study of such highly connected graphs that are, in…
An outer-1-planar graph is a graph admitting a drawing in the plane so that all vertices appear in the outer region of the drawing and every edge crosses at most one other edge. This paper establishes the local structure of outer-1-planar…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…