Results 11 to 20 of about 76,042 (299)
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
Abbe, Emmanuel, Wigderson, Yuval
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Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, 2011 This article considers the problem of computing a minimum weight cycle in weighted undirected graphs. Given a weighted undirected graph G = ( V , E , w ), let C be a minimum weight cycle of G , let
Liam Roditty, Roei Tov
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A stability result for girth‐regular graphs with even girth [PDF]
Journal of Graph Theory, 2021 AbstractLet denote a finite, connected, simple graph. For an edge of let denote the number of girth cycles containing . For a vertex of let be the set of edges incident to ordered such that . Then is called the signature of . The graph is said to be girth‐regular if all of its vertices have the same signature.
György Kiss +2 more
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Radius, girth and minimum degree [PDF]
Journal of Graph Theory, 2022 AbstractThe objective of the present paper is to study the maximum radius of a connected graph of order , minimum degree and girth at least . Erdős, Pach, Pollack and Tuza proved that if , that is, the graph is triangle‐free, then , and noted that up to the value of the additive constant, this upper bound is tight.
Dvorák, Vojtĕch +3 more
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Coloring Powers and Girth [PDF]
SIAM Journal on Discrete Mathematics, 2016 15 pages, 2 figures, 2 tables; from v1 to v2, one section removed, one theorem ...
Kang, J.R., Kang, J.R., Pirot, F.F.
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Computing Graph Roots Without Short Cycles [PDF]
, 2009 Graph G is the square of graph H if two vertices x, y have an edge in G if and only if x, y are of distance at most two in H. Given H it is easy to compute its square H2, however Motwani and Sudan proved that it is NP-complete to determine if a given ...
Farzad, Babak +3 more
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A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes
IEEE Access, 2021 In this article, we study the cycle structure of (3, 19)-regular Tanner’s quasi-cyclic (QC) LDPC codes with code length $19p$ , where $p$ is a prime and $p\equiv 1~(\bmod ~57)$ , and transform the conditions for the existence of cycles of ...
Manjie Zhou +4 more
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Exhaustive generation of $k$-critical $\mathcal H$-free graphs [PDF]
, 2015 We describe an algorithm for generating all $k$-critical $\mathcal H$-free graphs, based on a method of Ho\`{a}ng et al. Using this algorithm, we prove that there are only finitely many $4$-critical $(P_7,C_k)$-free graphs, for both $k=4$ and $k=5$.
B Randerath +17 more
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Ars Mathematica Contemporanea, 2019 20 pages, 6 ...
Potočnik, Primož, Vidali, Janoš
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Lower Bounds on the Lifting Degree of QC-LDPC Codes by Difference Matrices
IEEE Access, 2018 In this paper, we define two “difference matrices” which correspond to an exponent matrix. We present necessary and sufficient conditions for these difference matrices to have quasi-cyclic low-density parity-check codes (QC-LDPC) codes with
Farzane Amirzade, Mohammad-Reza Sadeghi
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