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Decompositions into subgraphs of small diameter
 Comb. Probab. Comput
"... We investigate decompositions of a graph into a small number of low diameter subgraphs. Let P(n, ǫ, d) be the smallest k such that every graph G = (V, E) on n vertices has an edge partition E = E0 ∪ E1 ∪... ∪ Ek such that E0  ≤ ǫn 2 and for all 1 ≤ i ≤ k the diameter of the subgraph spanned by Ei ..."
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Cited by 2 (1 self)
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We investigate decompositions of a graph into a small number of low diameter subgraphs. Let P(n, ǫ, d) be the smallest k such that every graph G = (V, E) on n vertices has an edge partition E = E0 ∪ E1 ∪... ∪ Ek such that E0  ≤ ǫn 2 and for all 1 ≤ i ≤ k the diameter of the subgraph spanned
Cubic Cayley graphs with small diameter
 Discrete Math. Theor. Comput. Sci
"... In this paper we apply Pólya’s Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group. We report the results of a search of all threeregular Cayley graphs on permutation groups of degree at most nine for small diamete ..."
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Cited by 1 (0 self)
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diameter graphs. We explore several methods of constructing covering graphs of these Cayley graphs. Examples of large graphs with small diameter are obtained.
Round SmallDiameter Timber for Construction
, 1999
"... The use of smalldiameter timber in construction has been investigated. The aim of the work is to increase the use of the wood harvested in forest thinning in construction applications. The work has covered a wide range of aspects, from availability of the material to design of the structures. This ..."
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The use of smalldiameter timber in construction has been investigated. The aim of the work is to increase the use of the wood harvested in forest thinning in construction applications. The work has covered a wide range of aspects, from availability of the material to design of the structures
Hydraulic Diameter of Compact Design Tubes with Small Diameter
"... Abstract: The contribution is aimed on hydraulic diameter of Compact Design Tubes with the small diameter. First part of contribution is focused on calculation of the hydraulic pipe diameter by contemporary way for technical use. Second part of contribution is aimed on Compact Design Tubes with the ..."
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Cited by 1 (0 self)
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Abstract: The contribution is aimed on hydraulic diameter of Compact Design Tubes with the small diameter. First part of contribution is focused on calculation of the hydraulic pipe diameter by contemporary way for technical use. Second part of contribution is aimed on Compact Design Tubes
NorthHolland Graphs with small diameter after
, 1992
"... Chung, F&K., Graphs with small diameter after edge deletion, Discrete Applied Mathematics 37/38 ..."
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Chung, F&K., Graphs with small diameter after edge deletion, Discrete Applied Mathematics 37/38
Treedecompositions with bags of small diameter
, 2007
"... This paper deals with the length of a Robertson–Seymour’s treedecomposition. The treelength of a graph is the largest distance between two vertices of a bag of a treedecomposition, minimized over all treedecompositions of the graph. The study of this invariant may be interesting in its own right ..."
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Cited by 19 (1 self)
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This paper deals with the length of a Robertson–Seymour’s treedecomposition. The treelength of a graph is the largest distance between two vertices of a bag of a treedecomposition, minimized over all treedecompositions of the graph. The study of this invariant may be interesting in its own right because the class of bounded treelength graphs includes (but is not reduced to) bounded chordality graphs (like interval graphs, permutation graphs, ATfree graphs, etc.). For instance, we show that the treelength of any outerplanar graph is ⌈k/3⌉, where k is the chordality of the graph, and we compute the treelength of meshes. More fundamentally we show that any algorithm computing a treedecomposition approximating the treewidth (or the treelength) of an nvertex graph by a factor α or less does not give an αapproximation of the treelength (resp. the treewidth) unless if α = Ω(n 1/5). We complete these results presenting several polynomial time constant approximate algorithms for the treelength. The introduction of this parameter is motivated by the design of compact distance labeling, compact routing tables with nearoptimal route length, and by the construction of sparse additive spanners.
Vertex Symmetric Digraphs with Small Diameter
 Discrete Appl. Math
, 1995
"... There is increasing interest in the design of dense vertex symmetric graphs and digraphs as models of interconnection networks for implementing parallelism. In these systems many nodes are connected with relatively few links and short paths between them and each node may execute, without modificatio ..."
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Cited by 16 (5 self)
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modifications, the same communication software. In this paper we give new families of dense vertex symmetric (#, D) digraphs, that is large digraphs with a given maximum outdegree # and diameter at most D. The digraphs are derived from a certain family of digraphs on alphabets, proposed by Faber and Moore [8
Domination in planar graphs with small diameter
 2002) 1–25. the electronic journal of combinatorics 10 (2003), #N9 5
"... MacGillivray and Seyffarth (J. Graph Theory 22 (1996), 213–229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrarily large do ..."
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Cited by 9 (1 self)
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MacGillivray and Seyffarth (J. Graph Theory 22 (1996), 213–229) proved that planar graphs of diameter two have domination number at most three and planar graphs of diameter three have domination number at most ten. They also give examples of planar graphs of diameter four having arbitrarily large
Surfaces of small diameter with large width
 J. Topol. Anal
"... Abstract. Given a 2dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M, g) ≤ 1 and every 1−cycle dividing M into two regions of equal area has length> C. It follows that there exists no universal inequality bounding 1−width of M in terms of its dia ..."
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Cited by 3 (1 self)
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Abstract. Given a 2dimensional surface M and a constant C we construct a Riemannian metric g, so that diameter diam(M, g) ≤ 1 and every 1−cycle dividing M into two regions of equal area has length> C. It follows that there exists no universal inequality bounding 1−width of M in terms of its
Small Diameter Membrane Reflector Structures
"... This paper proposes the use of membrane reflectors for space telescopes having apertures currently achievable using monolithic designs. It is shown, both analytically, and by numerical optimization, that membrane reflectors including necessary support structure may achieve comparable areal density ..."
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This paper proposes the use of membrane reflectors for space telescopes having apertures currently achievable using monolithic designs. It is shown, both analytically, and by numerical optimization, that membrane reflectors including necessary support structure may achieve comparable areal density to monolithic reflectors at a significantly reduced cost. Design formulae for the membrane reflector support structure are derived and validated. I.
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