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Extrinsic versus intrinsic diameter for Riemannian filling-discs and van Kampen diagrams
Riemannian filling-discs van Kampen diagrams
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2015/8/26
The diameter of a disc filling a loop in the universal covering of a Riemannian manifold M may be measured extrinsically using the distance function on the ambient space or intrinsically using the ind...
On the polygonal diameter of the interior, resp. exterior, of a simple closed polygon in the plane
Jordan-Brouwer theorem Jordan exterior (interior) Jordan’s curve theorem
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2011/2/21
We give a tight upper bound on the polygonal diameter of the interior, resp. exterior, of a simple n-gon, n ≥ 3, in the plane as a function of n, and describe an n-gon (n ≥ 3) for which both upper bou...
There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter
distance-regular graphs Bannai-Ito Conjecture
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2011/1/21
In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2
k ≤ C. This extends a conj...
The competition numbers of Hamming graphs with diameter at most three
Hamming graphs diameter
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2010/11/18
The competition graph of a digraph D is a graph which has the same vertex set as D and has an edge between x and y if and only if there exists a vertex v in D such that (x,v) and (y,v) are arcs of D. ...
The distribution of height and diameter in random non-plane binary trees
distribution of height diameter in random non-plane binary trees
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2010/12/1
This study is dedicated to precise distributional analyses of the height of non-plane unlabelled binary trees (“Otter trees”), when trees of a given size are taken with equal likelihood. The height of...
Geodesic diameter of sets defined by few quadratic equations and inequalities
Geodesic diameter of sets defined quadratic equations nequalities
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2010/11/29
We prove a bound for the geodesic diameter of a subset of the unit ball in Rn described by a fixed number of quadratic equations and inequalities,which is polynomial in n, whereas the known bound for ...
Classification of Regular Planar Graphs with Diameter two
graph regular diameter planar outer planar
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2007/12/11
In the present paper, the regular planar graphs with diameter two are classified.