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On the Chromatic Number of the Complement of a Class of Line Graphs
"... Let G beagraph, G its complement, L(G) its line graph, and χ(G) its chromatic number. Then we have the following Theorem Let G be agraph with n vertices. (i) If G is triangle free, then n − 4 ≤ χ L(G) ≤ n − 2 (ii) If G is planar and every triangle bounds a disk, then n − 3 ≤ χ L(G) ≤ n − 2 ..."
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Let G beagraph, G its complement, L(G) its line graph, and χ(G) its chromatic number. Then we have the following Theorem Let G be agraph with n vertices. (i) If G is triangle free, then n − 4 ≤ χ L(G) ≤ n − 2 (ii) If G is planar and every triangle bounds a disk, then n − 3 ≤ χ L(G) ≤ n − 2
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) ..."
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Cited by 2380 (22 self)
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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 ..."
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Cited by 801 (1 self)
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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
Multimarket Oligopoly: Strategic Substitutes and complements
 JOURNAL OF POLITICAL ECONOMY
"... A firm’s actions in one market can change competitors’ strategies in a second market by affecting its own marginal costs in that other market. Whether the action provides costs or benefits in the second market depends on (a) whether it increases or decreases marginal costs in the second market and ..."
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Cited by 601 (10 self)
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and (b) whether competitors’ products are strategic substitutes or strategic complements. The latter distinction is determined by whether more “aggressive” play (e.g., lower price or higher quantity) by one firm in a market lowers or raises competing firms’ marginal profitabilities in that market. Many
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 ..."
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Cited by 627 (44 self)
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graphs. These algorithms adopt a variety of representations (e.g., straightline, polyline, visibility), and update the drawing in a smooth way.
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. ..."
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Cited by 1173 (16 self)
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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.
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 ..."
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Cited by 822 (85 self)
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... 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
WordNet: An online lexical database
 International Journal of Lexicography
, 1990
"... WordNet is an online lexical reference system whose design is inspired by current ..."
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Cited by 1945 (9 self)
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WordNet is an online lexical reference system whose design is inspired by current
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 ..."
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Cited by 3499 (47 self)
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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
Results 1  10
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814,638