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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 ...
Given a two-dimensional smooth manifold M and a bijective pro jection p from M on a fixed plane (or a subset of that plane), we explore systematically how a wavelet transform (WT) on M may be generated from a plane WT by the inverse projection. Examples whe ...
In a drawing of a graph, two edges form an odd pair if they cross each other an odd number of times. A pair of edges is independent if they share no endpoint. For a graph G, let ocr(G) be the smallest number of odd pairs in a drawing of G and let iocr(G) b ...
The split-coloring problem is a generalized vertex coloring problem where we partition the vertices into a minimum number of split graphs. In this paper, we study some notions which are extensively studied for the usual vertex coloring and the cocoloring p ...
A drawing of a graph is x-monotone if every edge intersects every vertical line at most once and every vertical line contains at most one vertex. Pach and Toth showed that if a graph has an x-monotone drawing in which every pair of edges crosses an even nu ...
We settle a problem of Dujmovic, Eppstein, Suderman, and Wood by showing that there exists a function f with the property that every planar graph G with maximum degree d admits a drawing with noncrossing straight-line edges, using at most f(d) different sl ...
Springer-Verlag New York, Ms Ingrid Cunningham, 175 Fifth Ave, New York, Ny 10010 Usa2011
Let G = (V, E) be a graph with n vertices and m >= 4n edges drawn in the plane. The celebrated Crossing Lemma states that G has at least Omega(m(3)/n(2)) pairs of crossing edges; or equivalently, there is an edge that crosses Omega(m(2)/n(2)) other edges. ...
We here summarize some recent advances in the study of linear deterministic networks, recently proposed as approximations for wireless channels. This work started by extending the algebraic framework developed for multicasting over graphs in [1] to include ...
The Point Ahead Angle Mechanism (PAAM) for ESA’s Laser Interferometer Space Antenna (LISA) mission will compensate the out-of-plane point-ahead angle between three satellites flying 5 million kilometres apart. The PAAM consists of a mirror supported by fle ...
We develop new algebraic algorithms for scalar and vector network coding. In vector network coding, the source multicasts information by transmitting vectors of length L, while intermediate nodes process and combine their incoming packets by multiplying th ...
Institute of Electrical and Electronics Engineers2011
