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We define the crossing number for an embedding of a graph G into R^3, and prove a lower bound on it which almost implies the classical crossing lemma. We also give sharp bounds on the space crossing numbers of pseudo-random graphs. ...
The graph obtained from the integer grid Z x Z by the removal of all horizontal edges that do not belong to the x-axis is called a comb. In a random walk on a graph, whenever a walker is at a vertex v, in the next step it will visit one of the neighbors of ...
Various practical applications of the average (A) and difference (D) of Friedel opposites are described. Techniques based on the resonant-scattering contribution to Friedel differences are applied to see whether a crystal is centrosymmetric or not, and to ...
A drawing of a graph in the plane is called a thrackle if every pair of edges meets precisely once, either at a common vertex or at a proper crossing. Let t(n) denote the maximum number of edges that a thrackle of n vertices can have. According to a 40 yea ...
Developers often seek the origins of wrong values they see in their debugger. Their search must be backwards in time: the code causing the wrong value executed before the wrong value appeared. Searching with breakpoint- or log- based debuggers demands pers ...
We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends pe ...
We propose a new approach for describing the geometry information of multiview image representations. Rather than transmitting the raw geometry of the scene, under the form of depth information, we build a graph that represents the connections between corr ...
In this paper, we propose a representation and coding method for multiview images. As an alternative to depth-based schemes, we propose a representation that captures the geometry and the dependencies between pixels in different views in the form of connec ...
We consider communication of two degraded mes- sage sets over graphs where a common source sends two prioritized messages (a common and a private message) to several receivers. All receivers require the common message and a subset of the receivers require ...
A novel framework for image inpainting is proposed, relying on graph-based diffusion processes. Depending on the construction of the graph, both flow-based and exemplar-based inpainting methods can be implemented by the same equations, hence providing a un ...
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