Related papers: A 3-to-1 cactus graph: Details
A complete list of irreducible triangulations is identified on the M\"obius band.
The 3-Decomposition Conjecture states that every connected cubic graph can be decomposed into a spanning tree, a 2-regular subgraph and a matching. We show that this conjecture holds for the class of connected plane cubic graphs.
Damage scenarios for large networks are considered. The cascade scenario is described by means of powers of adjacency matrix. More difficult probabilistic variants of the large network damage are modeling by Markov chains. For reliability…
This paper presents considerations towards an information and control architecture for future electric energy systems driven by massive changes resulting from the societal goals of decarbonization and electrification. This paper describes…
This paper presents new results and reinterpretation of existing conditions for strong structural controllability in a structured network determined by the zero/non-zero patterns of edges. For diffusively-coupled networks with self-loops,…
We explore the geometry of complex networks in terms of an n-dimensional Euclidean embedding represented by the Moore-Penrose pseudo-inverse of the graph Laplacian $(\bb L^+)$. The squared distance of a node $i$ to the origin in this…
We explore the phenomenon of unidirectional invisibility in two dimensions, examine its optical realizations, and discuss its three-dimensional generalization. In particular we construct an infinite class of unidirectionally invisible…
We introduce a novel technique for checking reachability in Petri nets that relies on a recently introduced compositional algebra of nets. We prove that the technique is correct, and discuss our implementation. We report promising…
In comparing well-known CRDTs representing sets that can grow and shrink, we find caveats. In one, the removal of an element cannot be reliably undone. In another, undesirable states are attainable, such as when an element is present -1…
In the past, we have observed several large blackouts, i.e. loss of power to large areas. It has been noted by several researchers that these large blackouts are a result of a cascade of failures of various components. As a power grid is…
Flexible network design deals with building a network that guarantees some connectivity requirements between its vertices, even when some of its elements (like vertices or edges) fail. In particular, the set of edges (resp. vertices) of a…
We propose a network protocol similar to the $k$-tree protocol of Itai and Rodeh [{\em Inform.\ and Comput.}\ {\bf 79} (1988), 43--59]. To do this, we define an {\em $t$-uncovering-by-bases} for a connected graph $G$ to be a collection…
In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete…
We provide a finite equational presentation of graphs of treewidth at most three, solving an instanceof an open problem by Courcelle and Engelfriet. We use a syntax generalising series-parallel expressions, denoting graphs with a small…
When studying social, economic and biological systems, one has often access to only limited information about the structure of the underlying networks. An example of paramount importance is provided by financial systems: information on the…
This article describes the application of recently introduced complex networks concepts and methods to the characterization and analysis of cortical bone structure. Three-dimensional reconstructions of the system of channels underlying bone…
In this note we consider the survivable network design problem (SNDP) in undirected graphs. We make two contributions. The first is a new counting argument in the iterated rounding based 2-approximation for edge-connectivity SNDP (EC-SNDP)…
This paper studies \emph{Dirichlet arrangements}, a generalization of graphic hyperplane arrangements arising from electrical networks and order polytopes of finite posets. We generalize descriptions of combinatorial features of graphic…
The capacitance between any two arbitrary lattice sites in an infinite square lattice is studied when one bond is removed (i.e. perturbed). A connection is made between the capacitance and the Lattice Green's Function of the perturbed…
This paper is intended to provide an insight into physics and engineering that can modernize electric power systems. Topics covered are Flexible ac transmission systems (FACTS), Custom Power, Greatly improved Capacitors, Electrical…