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The complexity of theoremproving procedures
 IN STOC
, 1971
"... It is shown that any recognition problem solved by a polynomial timebounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology. Here “reduced ” means, roughly speaking, that the first problem can be solved deterministi ..."
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Cited by 1050 (5 self)
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of two given graphs is isomorphic to a subgraph of the second. Other examples are discussed. A method of measuring the complexity of proof procedures for the predicate calculus is introduced and discussed. Throughout this paper, a set of strings 1 means a set of strings on some fixed, large, finite
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 199 (11 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
The Average Distance in a Random Graph with Given Expected Degrees
"... Random graph theory is used to examine the “smallworld phenomenon”– any two strangers are connected through a short chain of mutual acquaintances. We will show that for certain families of random graphs with given expected degrees, the average distance is almost surely of order log n / log ˜ d whe ..."
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Cited by 289 (13 self)
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having some mild constraints for the average distance and maximum degree). In particular, these graphs contain a dense subgraph, that we call the core, having n c / log log n vertices. Almost all vertices are within distance log log n of the core although there are vertices at distance log n from
Colorful subgraphs of Kneserlike graphs
"... Combining Ky Fan’s theorem with ideas of Greene and Matouˇsek we prove a generalization of Dol’nikov’s theorem. Using another variant of the BorsukUlam theorem due to Bacon and Tucker, we also prove the presence of all possible completely multicolored tvertex complete bipartite graphs in tcolored ..."
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Cited by 9 (3 self)
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colored tchromatic Kneser graphs and in several of their relatives. In particular, this implies a generalization of a recent result of G. Spencer and The solution of Kneser’s conjecture in 1978 by László Lovász [19] opened up a new area of combinatorics that is usually referred to as the topological method
A Graph Distance Metric Based on the Maximal Common Subgraph
, 1998
"... Errortolerant graph matching is a powerful concept that has various applications in pattern recognition and machine vision. In the present paper, a new distance measure on graphs is proposed. It is based on the maximal common subgraph of two graphs. The new measure is superior to edit distance base ..."
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Cited by 174 (13 self)
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Errortolerant graph matching is a powerful concept that has various applications in pattern recognition and machine vision. In the present paper, a new distance measure on graphs is proposed. It is based on the maximal common subgraph of two graphs. The new measure is superior to edit distance
Maximal 4degenerated subgraph of a planar graph∗
, 2013
"... A graph G is kdegenerated if it can be deleted by subsequent removals of vertices of degree k or less. We prove that every planar graph of order n has a 4degenerated induced subgraph of order at least 8/9 · n. We also consider a local variation of this problem and show that in every planar graph w ..."
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A graph G is kdegenerated if it can be deleted by subsequent removals of vertices of degree k or less. We prove that every planar graph of order n has a 4degenerated induced subgraph of order at least 8/9 · n. We also consider a local variation of this problem and show that in every planar graph
Coloring Reduced Kneser Graphs
, 2003
"... The vertex set of a Kneser graph KG(m, n) consists of all nsubsets of the set [m] ={0, 1,...,m − 1}. Two vertices are defined to be adjacent if they are disjoint as subsets. A subset of [m] is called 2stable if 2 ≤a − b  ≤m − 2 for any distinct elements a and b in that subset. The reduced Kneser ..."
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Kneser graph KG2(m, n) is the subgraph of KG(m, n) induced by vertices that are 2stable subsets. We focus our study on the reduced Kneser graphs KG2(2n +2,n). We achieve a complete analysis of its structure. From there, we derive that the circular chromatic number of KG2(2n +2,n) is equal to its
Efficient influence maximization in social networks
 In Proc. of ACM KDD
, 2009
"... Influence maximization is the problem of finding a small subset of nodes (seed nodes) in a social network that could maximize the spread of influence. In this paper, we study the efficient influence maximization from two complementary directions. One is to improve the original greedy algorithm of [5 ..."
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Cited by 197 (18 self)
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of [5] and its improvement [7] to further reduce its running time, and the second is to propose new degree discount heuristics that improves influence spread. We evaluate our algorithms by experiments on two large academic collaboration graphs obtained from the online archival database arXiv.org. Our
Spin: Mining maximal frequent subgraphs from graph databases
 IN KDD
, 2004
"... One fundamental challenge for mining recurring subgraphs from semistructured data sets is the overwhelming abundance of such patterns. In large graph databases, the total number of frequent subgraphs can become too large to allow a full enumeration using reasonable computational resources. In this ..."
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Cited by 99 (12 self)
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reduces the total number of mined patterns by two to three orders of magnitude. Our method first mines all frequent trees from a general graph database and then reconstructs all maximal subgraphs from the mined trees. Using two chemical structure benchmarks and a set of synthetic graph data sets, we
Results 1  10
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1,786