Results 1  10
of
1,642,639
A better bound for the cop number of general graphs
 Journal of Graph Theory
, 2008
"... Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to ..."
Abstract

Cited by 22 (2 self)
 Add to MetaCart
Abstract: In this note,we prove that the cop number of any nvertex graph G, denoted by c(G), is at most O ( nlgn. Meyniel conjectured c(G) = O(√n). It appears that the best previously known sublinear upperbound is due to
Books in graphs
, 2008
"... A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α) ..."
Abstract

Cited by 2380 (22 self)
 Add to MetaCart
A set of q triangles sharing a common edge is called a book of size q. We write β (n, m) for the the maximal q such that every graph G (n, m) contains a book of size q. In this note 1) we compute β ( n, cn 2) for infinitely many values of c with 1/4 < c < 1/3, 2) we show that if m ≥ (1/4 − α
Community detection in graphs
, 2009
"... The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of th ..."
Abstract

Cited by 801 (1 self)
 Add to MetaCart
The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices
Interprocedural Slicing Using Dependence Graphs
 ACM TRANSACTIONS ON PROGRAMMING LANGUAGES AND SYSTEMS
, 1990
"... ... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends previou ..."
Abstract

Cited by 822 (85 self)
 Add to MetaCart
... This paper concerns the problem of interprocedural slicinggenerating a slice of an entire program, where the slice crosses the boundaries of procedure calls. To solve this problem, we introduce a new kind of graph to represent programs, called a system dependence graph, which extends
Graphbased algorithms for Boolean function manipulation
 IEEE TRANSACTIONS ON COMPUTERS
, 1986
"... In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on th ..."
Abstract

Cited by 3499 (47 self)
 Add to MetaCart
on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms have time complexity proportional
A fast and high quality multilevel scheme for partitioning irregular graphs
 SIAM JOURNAL ON SCIENTIFIC COMPUTING
, 1998
"... Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc. ..."
Abstract

Cited by 1173 (16 self)
 Add to MetaCart
Recently, a number of researchers have investigated a class of graph partitioning algorithms that reduce the size of the graph by collapsing vertices and edges, partition the smaller graph, and then uncoarsen it to construct a partition for the original graph [Bui and Jones, Proc.
A Framework for Dynamic Graph Drawing
 CONGRESSUS NUMERANTIUM
, 1992
"... Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized as follows ..."
Abstract

Cited by 627 (44 self)
 Add to MetaCart
Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized
The program dependence graph and its use in optimization
 ACM Transactions on Programming Languages and Systems
, 1987
"... In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program. ..."
Abstract

Cited by 989 (3 self)
 Add to MetaCart
In this paper we present an intermediate program representation, called the program dependence graph (PDG), that makes explicit both the data and control dependence5 for each operation in a program. Data dependences have been used to represent only the relevant data flow relationships of a program
Mining Generalized Association Rules
, 1995
"... We introduce the problem of mining generalized association rules. Given a large database of transactions, where each transaction consists of a set of items, and a taxonomy (isa hierarchy) on the items, we find associations between items at any level of the taxonomy. For example, given a taxonomy th ..."
Abstract

Cited by 577 (7 self)
 Add to MetaCart
We introduce the problem of mining generalized association rules. Given a large database of transactions, where each transaction consists of a set of items, and a taxonomy (isa hierarchy) on the items, we find associations between items at any level of the taxonomy. For example, given a taxonomy
Results 1  10
of
1,642,639