Results 51 to 60 of about 24,879 (166)
Boxicity and Cubicity of Product Graphs
, 2013 The 'boxicity' ('cubicity') of a graph G is the minimum natural number k such that G can be represented as an intersection graph of axis-parallel rectangular boxes (axis-parallel unit cubes) in $R^k$.
Chandran, L. Sunil +3 more
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On the Number of Errors Correctable with Codes on Graphs
, 2011 We study ensembles of codes on graphs (generalized low-density parity-check, or LDPC codes) constructed from random graphs and fixed local constrained codes, and their extension to codes on hypergraphs.
Barg, Alexander, Mazumdar, Arya
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MathematicsWe consider mixed Hamming packings, addressing the maximal cardinality of codes with a minimum codeword Hamming distance. We do not rely on any algebraic structure of the alphabets.
Péter Naszvadi +2 more
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Algorithms for the Shortest Path Improvement Problems under Unit Hamming Distance
Journal of Applied Mathematics, 2013 In a shortest path improvement problem under unit Hamming distance (denoted by SPIUH), an edge weighted graph with a set of source-terminal pairs is given; we need to modify the lengths of edges by a minimum cost under unit Hamming distance such that the
Bingwu Zhang +3 more
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On the binary codes with parameters of triply-shortened 1-perfect codes
, 2011 We study properties of binary codes with parameters close to the parameters of 1-perfect codes. An arbitrary binary $(n=2^m-3, 2^{n-m-1}, 4)$ code $C$, i.e., a code with parameters of a triply-shortened extended Hamming code, is a cell of an equitable ...
D.S. Krotov +7 more
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, 2011 We consider the problem of computing all-pairs shortest paths in a directed graph with real weights assigned to vertices. For an $n\times n$ 0-1 matrix $C,$ let $K_{C}$ be the complete weighted graph on the rows of $C$ where the weight of an edge ...
Lingas, Andrzej, Sledneu, Dzmitry
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On Robust Colorings of Hamming-Distance Graphs [PDF]
The Electronic Journal of Combinatorics, 2018 $H_q(n,d)$ is defined as the graph with vertex set $\mathbb{Z}_q^n$ and where two vertices are adjacent if their Hamming distance is at least $d$. The chromatic number of these graphs is presented for various sets of parameters $(q,n,d)$. For the $4$-colorings of the graphs $H_2(n,n-1)$ a notion of robustness is introduced. It is based on the tolerance
Harney, Isaiah, Gluesing-Luerssen, Heide
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Randomized Communication and Implicit Graph Representations [PDF]
TheoretiCSWe initiate the focused study of constant-cost randomized communication, with emphasis on its connection to graph representations. We observe that constant-cost randomized communication problems are equivalent to hereditary (i.e.
Nathaniel Harms +2 more
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Graphs and CombinatoricsThe Hamming graph $H(n,q)$ is defined on the vertex set $[q]^n$ and two vertices are adjacent if and only if they differ in precisely one coordinate. Alon \cite{Alon} proved that the burning number of $H(n,2)$ is $\lceil\frac n2\rceil+1$. In this note we give a short proof of a fact that the burning number of $H(n,q)$ is $(1-\frac 1q)n+O(\sqrt{n\log n})
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Open Geosciences, 2018 This paper presented a new method for identifying promising areas for archaeological research. The method is based on graph analysis that iteratively compares and manipulates Hamming distances between graphs of input geographical parameters and graphs of
Mertel Adam +2 more
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