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298,969
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 1048 (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
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
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
On finite simple groups and Kneser graphs
 J. Algebr. Comb
"... Abstract. For a finite group G let Γ(G) be the (simple) graph defined on the elements of G with an edge between two (distinct) vertices if and only if they generate G. The chromatic number of Γ(G) is considered for various nonsolvable groups G. 1. ..."
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Cited by 3 (2 self)
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Abstract. For a finite group G let Γ(G) be the (simple) graph defined on the elements of G with an edge between two (distinct) vertices if and only if they generate G. The chromatic number of Γ(G) is considered for various nonsolvable groups G. 1.
Graphs cospectral with Kneser graphs
, 2009
"... We construct graphs that are cospectral but nonisomorphic with Kneser graphs K(n, k), when n = 3k − 1, k> 2 and for infinitely many other pairs (n, k). We also prove that for 3 ≤ k ≤ n − 3 the Modulo2 Kneser graph K2(n, k) is not determined by the spectrum. ..."
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We construct graphs that are cospectral but nonisomorphic with Kneser graphs K(n, k), when n = 3k − 1, k> 2 and for infinitely many other pairs (n, k). We also prove that for 3 ≤ k ≤ n − 3 the Modulo2 Kneser graph K2(n, k) is not determined by the spectrum.
Symmetries of the stable kneser graphs
 Advances in Applied Mathematics, 45(1):12
"... Abstract. It is well known that the automorphism group of the Kneser graph KGn,k is the symmetric group on n letters. For n ≥ 2k + 1, k ≥ 2, we prove that the automorphism group of the stable Kneser graph SGn,k is the dihedral group of order 2n. Let [n]: = [1, 2, 3,..., n]. For each n ≥ 2k, n, k ∈ { ..."
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Cited by 4 (2 self)
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∈ {1, 2, 3,...}, the Kneser graph KGn,k has as vertices the ksubsets of [n] with edges defined by disjoint pairs of ksubsets. For the same parameters, the stable Kneser graph SGn,k is the subgraph of KGn,k induced by the stable ksubsets of [n], i.e. those subsets that do not contain any 2subset
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 287 (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 173 (12 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
Applications of Stress Theory: Realizing Graphs and KneserPoulsen
, 2005
"... We use the ideas of stress theory and tensegrities to answer some questions in discrete geometry. In particular, we classify 3realizable graphs and we show some results related to the KneserPoulsen conjecture in hyperbolic space. A graph is drealizable if, for every configuration of its vertices ..."
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Cited by 1 (1 self)
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We use the ideas of stress theory and tensegrities to answer some questions in discrete geometry. In particular, we classify 3realizable graphs and we show some results related to the KneserPoulsen conjecture in hyperbolic space. A graph is drealizable if, for every configuration of its vertices
Results 1  10
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298,969