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Culturel Heritage "Girth Weaving" and Excamples of Girth Weaving From
, 2013 Kahvecioglu Sari, H, Bas, Y
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Canadian Mathematical Bulletin, 1982
AbstractLower bounds are given for the independence ratio in graphs satisfying certain girth and maximum degree requirements. In particular, the independence ratio of a graph with maximum degree Δ and girth at least six is at least (2Δ − 1)/(Δ2 + 2Δ − 1). Sharper bounds are given for cubic graphs.
Hopkins, Glenn, Staton, William
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AbstractLower bounds are given for the independence ratio in graphs satisfying certain girth and maximum degree requirements. In particular, the independence ratio of a graph with maximum degree Δ and girth at least six is at least (2Δ − 1)/(Δ2 + 2Δ − 1). Sharper bounds are given for cubic graphs.
Hopkins, Glenn, Staton, William
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Girth and Euclidean distortion
Geometric And Functional Analysis, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Linial, Nathan +2 more
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AJN, American Journal of Nursing, 2012
Addressing obesity requires more than self-control.
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Addressing obesity requires more than self-control.
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Journal of Graph Theory, 1989
AbstractLet G be 2‐connected graph with girth g and minimum degree d. Then each pair of vertices of G is joined by a path of length at least max{1/2(d − 1)g, (d − 3/2)(g − 4) + 2} if g ⩾ 4, and the length of a longest cycle of G is at least max{[(d − 1)(g − 2) + 2], [(2d − 3)(g − 4) + 4]}.
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AbstractLet G be 2‐connected graph with girth g and minimum degree d. Then each pair of vertices of G is joined by a path of length at least max{1/2(d − 1)g, (d − 3/2)(g − 4) + 2} if g ⩾ 4, and the length of a longest cycle of G is at least max{[(d − 1)(g − 2) + 2], [(2d − 3)(g − 4) + 4]}.
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A High Girth Graph Construction
SIAM Journal on Discrete Mathematics, 2003Summary: We give a deterministic algorithm that constructs a graph of girth \(\log_{k}(n) + O(1)\) and minimum degree \(k-1\), taking number of nodes \(n\) and number of edges \(e =\lfloor nk / 2\rfloor\) (where \(k < \frac{n}{3}\)) as input. The degree of each node is guaranteed to be \(k-1\), \(k\), or \(k+1\), where \(k\) is the average degree ...
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