Results 1  10
of
135,982
The Moore bound for irregular graphs
 Graphs Combin
, 2001
"... What is the largest number of edges in a graph of order n and girth g? For dregular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an armative answer to an old open problem ([4] p.163, problem 10). ..."
Abstract

Cited by 60 (7 self)
 Add to MetaCart
What is the largest number of edges in a graph of order n and girth g? For dregular graphs, essentially the best known answer is provided by the Moore bound. This result is extended here to cover irregular graphs as well, yielding an armative answer to an old open problem ([4] p.163, problem 10).
HIGHER DIMENSIONAL MOORE BOUNDS
, 906
"... Abstract. We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs. 1. ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
Abstract. We prove upper bounds on the face numbers of simplicial complexes in terms on their girths, in analogy with the Moore bound from graph theory. Our definition of girth generalizes the usual definition for graphs. 1.
The Moore bound for Spectral Radius
, 2008
"... Let G be a graph with n vertices, m edges, and girth g. If µ is the largest eigenvalue of the adjacency matrix of G, then µ + µ (µ − 1) · · · + µ (µ − 1) r−1 { n − 1 if g = 2r + 1 m if g = 2r. In particular, this inequality extends a result of Alon, Hoory, and Linial on the Moore bound of irregul ..."
Abstract
 Add to MetaCart
Let G be a graph with n vertices, m edges, and girth g. If µ is the largest eigenvalue of the adjacency matrix of G, then µ + µ (µ − 1) · · · + µ (µ − 1) r−1 { n − 1 if g = 2r + 1 m if g = 2r. In particular, this inequality extends a result of Alon, Hoory, and Linial on the Moore bound
A Moore bound for simplicial complexes
 BULL. LONDON MATH. SOC
"... Let X be a ddimensional simplicial complex with N faces of dimension (d − 1). Suppose that any (d − 1)face of X is contained in at least k ≥ d+ 2 faces of X of dimension d. Extending the classical Moore bound for graphs, it is shown that X must contain a ball B of radius at most dlogk−dNe such th ..."
Abstract

Cited by 9 (2 self)
 Add to MetaCart
Let X be a ddimensional simplicial complex with N faces of dimension (d − 1). Suppose that any (d − 1)face of X is contained in at least k ≥ d+ 2 faces of X of dimension d. Extending the classical Moore bound for graphs, it is shown that X must contain a ball B of radius at most dlogk
Digraphs of degree 3 and order close to the Moore bound
, 1995
"... It is known that Moore digraphs of degree d ? 1 and diameter k ? 1 do not exist (see [20] or [5]). Furthermore, for degree 2, it is shown that for k 3 there are no digraphs of order `close' to, i.e., one less than, Moore bound [18]. In this paper, we shall consider digraphs of diameter k, degr ..."
Abstract

Cited by 10 (6 self)
 Add to MetaCart
It is known that Moore digraphs of degree d ? 1 and diameter k ? 1 do not exist (see [20] or [5]). Furthermore, for degree 2, it is shown that for k 3 there are no digraphs of order `close' to, i.e., one less than, Moore bound [18]. In this paper, we shall consider digraphs of diameter k
On the structure of digraphs with order close to the Moore bound
, 1996
"... The Moore bound for a diregular digraph of degree d and diameter k is M d;k = 1 + d + : : : + d k . It is known that digraphs of order M d;k do not exist for d ? 1 and k ? 1 ([24] or [6]). In this paper we study digraphs of degree d, diameter k and order M d;k \Gamma 1, denoted by (d; k)digraphs ..."
Abstract

Cited by 9 (5 self)
 Add to MetaCart
The Moore bound for a diregular digraph of degree d and diameter k is M d;k = 1 + d + : : : + d k . It is known that digraphs of order M d;k do not exist for d ? 1 and k ? 1 ([24] or [6]). In this paper we study digraphs of degree d, diameter k and order M d;k \Gamma 1, denoted by (d; k
Monotone Complexity
, 1990
"... We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a simple ..."
Abstract

Cited by 2837 (11 self)
 Add to MetaCart
We give a general complexity classification scheme for monotone computation, including monotone spacebounded and Turing machine models not previously considered. We propose monotone complexity classes including mAC i , mNC i , mLOGCFL, mBWBP , mL, mNL, mP , mBPP and mNP . We define a
The Complete Atomic Structure of the Large Ribosomal Subunit at 2.4 Å Resolution
 Science
, 2000
"... ation, and termination phases of protein synthesis. Because the structures of several DNA and RNA polymerases have been determined at atomic resolution, the mechanisms of DNA and RNA synthesis are both well understood. Determination of the structure of the ribosome, however, has proven a daunting t ..."
Abstract

Cited by 529 (13 self)
 Add to MetaCart
and nucleic acids that assist in protein synthesis bound to the ribosome (3). Earlier this yea
Results 1  10
of
135,982