Results 11 to 20 of about 57,717 (241)
High-Girth matrices and polarization [PDF]
2015 IEEE International Symposium on Information Theory (ISIT), 2015 The girth of a matrix is the least number of linearly dependent columns, in contrast to the rank which is the largest number of linearly independent columns. This paper considers the construction of {\it high-girth} matrices, whose probabilistic girth is close to its rank.
Emmanuel Abbe, Yuval Wigderson
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High girth and extendability [PDF]
Discrete Mathematics, 1996 A graph \(G\) is said to be \(k\)-extendable if \(G\) contains a perfect matching, has more than \(2k\) vertices, and every matching of size \(k\) can be extended to a perfect matching. This concept was introduced by \textit{M. D. Plummer} [Discrete Math. 31, 201-210 (1980; Zbl 0442.05060)]. The main result is that for positive integers \(n\) and \(k\)
Pavol Gvozdjak, Jaroslav Nesetril
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Constructing Large Girth QC Protograph LDPC Codes Based on PSD-PEG Algorithm
IEEE Access, 2017 For a given base graph, the lifted graph can be obtained by a copy-and-permute procedure. If the permutation is cyclic, the lifted graph corresponds to a quasi-cyclic (QC) protograph low-density parity-check (LDPC) code.
Xue-Qin Jiang +3 more
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Ars Mathematica Contemporanea, 2019 20 pages, 6 ...
Primoz Potocnik, Janos Vidali
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A revival of the girth conjecture [PDF]
Journal of Combinatorial Theory, Series B, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tomás Kaiser +2 more
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Tanner
IEEE Access, 2019 Girth plays an important role in the design of low-density parity-check (LDPC) codes. Motivated by the works on the girth of some classes of Tanner quasi-cyclic (QC) LDPC codes, e.g., Tanner (3, 5), (3, 7), (3, 11), and (5, 7) codes, we, in this paper ...
Hengzhou Xu +4 more
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On the girth of digraphs [PDF]
Discrete Mathematics, 2000 Let \(G\) denote a strongly-connected digraph with \(n\) nodes, girth \(g\), and diameter \(D\). The author shows that if \(G\) has \(t\) nodes of out-degree one, then \(D\leq n-g+ t\). He also shows that if \(r\) denotes the minimum out-degree of \(G\), then \(g\leq \max\{\lceil n/r\rceil, 2r- 2\}\). This last result implies that when \(n\geq 2r^2- 3r+
Shen, Jian, Jian Shen
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Counterexamples to Borsuk’s Conjecture with Large Girth [PDF]
Mathematical Notes, 2019 Borsuk’s celebrated conjecture, which has been disproved, can be stated as follows: in ℝn, there exist no diameter graphs with chromatic number larger than n + 1. In this paper, we prove the existence of counterexamples to Borsuk’s conjecture which, in
R. Prosanov
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Large-Girth Roots of Graphs [PDF]
SIAM Journal on Discrete Mathematics, 2010 14 pages, 4 ...
Anna Adamaszek, Michal Adamaszek
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On the girth of infinite graphs [PDF]
Discrete Mathematics, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Seifter, Norbert, Norbert Seifter
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