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Block Graphs in Practice
"... Motivated by the rapidly increasing size of genomic databases, code repositories and versioned texts, several compression schemes have been proposed that work well on highlyrepetitive strings and also support fast random access: e.g., LZEnd, RLZ, GDC, augmented SLPs, and block graphs. Block graphs ..."
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Cited by 1 (1 self)
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Motivated by the rapidly increasing size of genomic databases, code repositories and versioned texts, several compression schemes have been proposed that work well on highlyrepetitive strings and also support fast random access: e.g., LZEnd, RLZ, GDC, augmented SLPs, and block graphs. Block
Bandwidth And Density For Block Graphs
 Nature Biotechnol
, 1996
"... . The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special class of block graphs (graphs in which every block is a cli ..."
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Cited by 5 (0 self)
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. The bandwidth of a graph G is the minimum of the maximum difference between adjacent labels when the vertices have distinct integer labels. We provide a polynomial algorithm to produce an optimal bandwidth labeling for graphs in a special class of block graphs (graphs in which every block is a
Sum list coloring block graphs
 Graphs Combin
"... Abstract. A graph is fchoosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize fchoosable functions for block graphs (graphs in which each block is a clique, including trees and line graphs of trees). The sum ..."
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Cited by 6 (0 self)
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Abstract. A graph is fchoosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. We characterize fchoosable functions for block graphs (graphs in which each block is a clique, including trees and line graphs of trees). The sum
On the adjacency matrix of a block graph
, 2013
"... A block graph is a graph in which every block is a complete graph. Let G be a block graph and let A be the adjacency matrix of G. We first obtain a formula for the determinant of A over reals. It is shown that A is nonsingular over IF2 if and only if the removal of any vertex from G produces a graph ..."
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A block graph is a graph in which every block is a complete graph. Let G be a block graph and let A be the adjacency matrix of G. We first obtain a formula for the determinant of A over reals. It is shown that A is nonsingular over IF2 if and only if the removal of any vertex from G produces a
Uniquely monopolarpartitionable block graphs
, 2013
"... As a common generalization of bipartite and split graphs, monopolar graphs are defined in terms of the existence of certain vertex partitions. It has been shown that to determine whether a graph has such a partition is an NPcomplete problem for general graphs, and is polynomial time solvable for se ..."
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for several classes of graphs. In this paper, we investigate graphs that admit a unique such partition and call them uniquely monopolarpartitionable graphs. By employing a tree trimming technique, we obtain a characterization of uniquely monopolarpartitionable block graphs. Our characterization implies a
Isometricpath numbers of block graphs
, 2004
"... An isometric path between two vertices in a graph G is a shortest path joining them. The isometricpath number of G, denoted by ip(G), is the minimum number of isometric paths required to cover all vertices of G. In this paper, we determine exact values of isometricpath numbers of block graphs. We ..."
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An isometric path between two vertices in a graph G is a shortest path joining them. The isometricpath number of G, denoted by ip(G), is the minimum number of isometric paths required to cover all vertices of G. In this paper, we determine exact values of isometricpath numbers of block graphs. We
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
Factor Graphs and the SumProduct Algorithm
 IEEE TRANSACTIONS ON INFORMATION THEORY
, 1998
"... A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple c ..."
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Cited by 1787 (72 self)
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A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple
Results 1  10
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516,161