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SelfDefinable Claw Free Functions
, 1996
"... . We propose a new type of claw free function family, a pseudo selfdefinable claw free function family , which provides, by Damgard's construction, a collision intractable hash function family that is more suitable in several cryptographic applications such as digital signature, bit commitment ..."
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. We propose a new type of claw free function family, a pseudo selfdefinable claw free function family , which provides, by Damgard's construction, a collision intractable hash function family that is more suitable in several cryptographic applications such as digital signature, bit
Quantum Cryptanalysis of Hash and ClawFree Functions
 ACM Sigact News
, 1997
"... . We give a quantum algorithm that finds collisions in arbitrary rtoone functions after only O( 3 p N=r ) expected evaluations of the function, where N is the cardinality of the domain. Assuming the function is given by a black box, this is more efficient than the best possible classical algori ..."
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Cited by 36 (0 self)
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algorithm, even allowing probabilism. We also give a similar algorithm for finding claws in pairs of functions. Further, we exhibit a spacetime tradeoff for our technique. Our approach uses Grover's quantum searching algorithm in a novel way. 1 Introduction A collision for function F : X ! Y consists
How to Construct ConstantRound ZeroKnowledge Proof Systems for NP
 Journal of Cryptology
, 1995
"... Constantround zeroknowledge proof systems for every language in NP are presented, assuming the existence of a collection of clawfree functions. In particular, it follows that such proof systems exist assuming the intractability of either the Discrete Logarithm Problem or the Factoring Problem for ..."
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Cited by 169 (8 self)
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Constantround zeroknowledge proof systems for every language in NP are presented, assuming the existence of a collection of clawfree functions. In particular, it follows that such proof systems exist assuming the intractability of either the Discrete Logarithm Problem or the Factoring Problem
ClawFree Graphs  a Survey.
, 1996
"... In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden subgraph ..."
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Cited by 12 (1 self)
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In this paper we summarize known results on clawfree graphs. The paper is subdivided into the following chapters and sections: 1. Introduction 2. Paths, cycles, hamiltonicity a) Preliminaries b) Degree and neighborhood conditions c) Local connectivity conditions d) Further forbidden
On ffactors in clawfree graphs
 AUSTRALASIAN JOURNAL OF COMBINATORICS VOLUME 52 (2012), PAGES 133–140
, 2012
"... Let G be a 2connected clawfree graph such that δ(G) ≥ 5. Then for every function f: V (G) →{1, 2}, where ∑ x∈V (G) f(x) is even, G has an ffactor. ..."
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Let G be a 2connected clawfree graph such that δ(G) ≥ 5. Then for every function f: V (G) →{1, 2}, where ∑ x∈V (G) f(x) is even, G has an ffactor.
Counting clawfree cubic graphs
"... Abstract. Let Hn be the number of clawfree cubic graphs on 2n labeled nodes. Combinatorial reductions are used to derive a second order, linear homogeneous differential equation with polynomial coefficients whose power series solution is the exponential generating function for {Hn}. This leads to a ..."
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Cited by 3 (1 self)
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Abstract. Let Hn be the number of clawfree cubic graphs on 2n labeled nodes. Combinatorial reductions are used to derive a second order, linear homogeneous differential equation with polynomial coefficients whose power series solution is the exponential generating function for {Hn}. This leads
Clawfree Graphs VI. Colouring
, 2011
"... In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can be ..."
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Cited by 4 (0 self)
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In this paper we prove that if G is a connected clawfree graph with three pairwise nonadjacent vertices, with chromatic number χ and clique number ω, then χ ≤ 2ω and the same for the complement of G. We also prove that the choice number of G is at most 2ω, except possibly in the case when G can
Clique minors in clawfree graphs
 J. Combin. Theory Ser. B
"... Hadwiger’s conjecture states that every graph with chromatic number χ has a clique minor of size χ. Let G be a graph on n vertices with chromatic number χ and stability number α. Then since χα ≥ n, Hadwiger’s conjecture implies that G has a clique minor of size n α. In this paper we prove that this ..."
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Cited by 1 (0 self)
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that this is true for connected clawfree graphs with α ≥ 3. We also show that this result is tight by providing an infinite family of clawfree graphs with α ≥ 3 that do not have a clique minor of size larger than n α
IMextendable Clawfree Graphs
 J. Mathematics Study
, 1999
"... Abstract. A graph G is kclawfree if no vertex has k pairwise nonadjacent neighbors. A proper kcoloring of G is a map from the vertex set to a set of k colors such that no two adjacent vertices map to the same color. The chromatic number χ(G) is the minimal k such that a proper kcoloring of G exi ..."
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Cited by 1 (0 self)
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(G) = 2. Therefore in general we cannot bound χ(G) above by a function of ω(G). In 2005, Chudnovsky and Seymour showed that if G is 3clawfree with α(G) ≥ 3, then χ(G) ≤ 2ω(G). We extend this result to kclawfree graphs. A 4hole is four vertices joined together in a square, but neither
ClawFree Graphs With Complete Closure
, 1999
"... We study some properties of the closure concept in clawfree graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite classes of nonpancyclic graphs with pancyclic closure. We show several ..."
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Cited by 1 (0 self)
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We study some properties of the closure concept in clawfree graphs that was introduced by the first author. It is known that G is hamiltonian if and only if its closure is hamiltonian, but, on the other hand, there are infinite classes of nonpancyclic graphs with pancyclic closure. We show several
Results 1  10
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14,080