Results 11 to 20 of about 415,247 (217)
Discrete Mathematics, 1990 AbstractUnit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set ...
Charles J. Colbourn +5 more
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Loewner chains in the unit disk
Revista Matemática Iberoamericana, 2010 In this paper we introduce a general version of the notion of Loewner chains which comes from the new and unified treatment, given in [Bracci, F., Contreras, M.D. and Díaz-Madrigal, S.: Evolution families and the Loewner equation I: the unit disk. To appear in J. Reine Angew. Math.] of the radial and chordal variant of the Loewner differential equation,
Contreras M. D. +2 more
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Improper colouring of (random) unit disk graphs [PDF]
Discrete Mathematics, 2005 For any graph $G$, the $k$-improper chromatic number $χ ^k(G)$ is the smallest number of colours used in a colouring of $G$ such that each colour class induces a subgraph of maximum degree $k$. We investigate the ratio of the $k$-improper chromatic number to the clique number for unit disk graphs and random unit disk graphs to extend results of [McRe99,
Kang, Ross, J. +2 more
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Contraction of the matrix unit disk
Linear Algebra and its Applications, 1986 AbstractA Möbius transformation M that is J-equivalent to a contraction, decreases the pseudochordal distance between every pair of points in the unit (matrix) disk. It may keep unchanged the distance between some pairs, and strictly decrease the distance between others.
Binyamin Schwarz, Abraham Zaks
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Harmonic automorphisms of the unit disk
Journal of Computational and Applied Mathematics, 1999 AbstractLet H be the class of harmonic automorphisms of the unit disk D. The function F=h−g associated with f=h+ḡ∈H maps D conformally onto a horizontally convex domain Ω. Conversely, given Ω both f∈H and F with F(D)=Ω can be retrieved (Theorem 1). Compact subclasses H(M)⊂H consisting of Poisson extensions of M-quasisymmetric automorphisms of ∂D span ...
Jan G. Krzyż, Maria Nowak
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Limits of Zeros of Orthogonal Polynomials on the Circle [PDF]
, 2004 We prove that there is a universal measure on the unit circle such that any probability measure on the unit disk is the limit distribution of some subsequence of the corresponding orthogonal polynomials.
Simon, Barry, Totik, Vilmos
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, 2010 We present two new approximation algorithms with (improved) constant ratios for selecting $n$ points in $n$ unit disks such that the minimum pairwise distance among the points is maximized. (I) A very simple $O(n \log{n})$-time algorithm with ratio 0.5110 for disjoint unit disks. In combination with an algorithm of Cabello \cite{Ca07}, it yields a $O(n^
Dumitrescu, Adrian, Jiang, Minghui
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THE FILLING DISKS OF AN ALGEBROID FUNCTION IN THE UNIT DISK [PDF]
Bulletin of the Australian Mathematical Society, 2010 AbstractUsing potential theory, we prove the existence of filling disks of an algebroid function of finite order defined in the unit disk.
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Evaluating polynomials over the unit disk and the unit ball [PDF]
Numerical Algorithms, 2013 19 pages, 3 ...
David Chien +2 more
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Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete [PDF]
, 2013 We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges.
J. Díaz, P. Bose, R. Tamassia
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