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Vertex decompositions of sparse graphs into an edgeless subgraph and a subgraph of maximum degree at most k
, 2010
"... A graph G is (k, 0)colorable if its vertices can be partitioned into subsets V1 and V2 such that in G[V1] every vertex has degree at most k, while G[V2] is edgeless. For every integer k ≥ 1, we prove that every graph with the maximum average degree smaller than 3k+4 is (k,0)colorable. k+2 In parti ..."
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Cited by 9 (6 self)
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A graph G is (k, 0)colorable if its vertices can be partitioned into subsets V1 and V2 such that in G[V1] every vertex has degree at most k, while G[V2] is edgeless. For every integer k ≥ 1, we prove that every graph with the maximum average degree smaller than 3k+4 is (k,0)colorable. k+2
VERTEX DECOMPOSITIONS OF SPARSE GRAPHS INTO AN INDEPENDENT VERTEX SET AND A SUBGRAPH OF MAXIMUM DEGREE AT MOST 1
, 2011
"... A graph G is (1, 0)colorable if its vertex set can be partitioned into subsets V1 and V0 so that in G[V1] every vertex has degree at most 1, while G[V0] is edgeless. We prove that every graph with maximum average degree at most 12 5 is (1, 0)colorable. In particular, every planar graph with girth ..."
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Cited by 2 (0 self)
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A graph G is (1, 0)colorable if its vertex set can be partitioned into subsets V1 and V0 so that in G[V1] every vertex has degree at most 1, while G[V0] is edgeless. We prove that every graph with maximum average degree at most 12 5 is (1, 0)colorable. In particular, every planar graph with girth
Frequent Subgraph Discovery
, 2001
"... Over the years, frequent itemset discovery algorithms have been used to solve various interesting problems. As data mining techniques are being increasingly applied to nontraditional domains, existing approaches for finding frequent itemsets cannot be used as they cannot model the requirement of th ..."
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Cited by 407 (14 self)
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of these domains. An alternate way of modeling the objects in these data sets, is to use a graph to model the database objects. Within that model, the problem of finding frequent patterns becomes that of discovering subgraphs that occur frequently over the entire set of graphs. In this paper we present a
The Dense kSubgraph Problem
 Algorithmica
, 1999
"... This paper considers the problem of computing the dense kvertex subgraph of a given graph, namely, the subgraph with the most edges. An approximation algorithm is developed for the problem, with approximation ratio O(n ffi ), for some ffi ! 1=3. 1 Introduction We study the dense ksubgraph (D ..."
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Cited by 205 (12 self)
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(DkS) maximization problem, of computing the dense k vertex subgraph of a given graph. That is, on input a graph G and a parameter k, we are interested in finding a set of k vertices with maximum average degree in the subgraph induced by this set. As this problem is NPhard (say, by reduction from
A Critical Point For Random Graphs With A Given Degree Sequence
, 2000
"... Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0 the ..."
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Cited by 511 (8 self)
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Given a sequence of nonnegative real numbers 0 ; 1 ; : : : which sum to 1, we consider random graphs having approximately i n vertices of degree i. Essentially, we show that if P i(i \Gamma 2) i ? 0 then such graphs almost surely have a giant component, while if P i(i \Gamma 2) i ! 0
AN n 5/2 ALGORITHM FOR MAXIMUM MATCHINGS IN BIPARTITE GRAPHS
, 1973
"... The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. ..."
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Cited by 712 (1 self)
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The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/.
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
Forbidden Subgraph Decomposition
 DISCRETE MATHEMATICS
, 1999
"... We define a new form of graph decomposition, based on forbidding a fixed bipartite graph from occurring as an induced subgraph of edges which cross a partition of the vertices. We show that some natural decompositions obtained in this way (including the generalized join proposed by Hsu [6]) are N ..."
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Cited by 1 (0 self)
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We define a new form of graph decomposition, based on forbidding a fixed bipartite graph from occurring as an induced subgraph of edges which cross a partition of the vertices. We show that some natural decompositions obtained in this way (including the generalized join proposed by Hsu [6
Results 1  10
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44,359