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The Complexity of Counting Graph Homomorphisms
 In 11th ACM/SIAM Symposium on Discrete Algorithms
, 1999
"... The problem of counting graph homomorphisms is considered. We show that the counting problem corresponding to a given graph is #Pcomplete unless every connected component of the graph is an isolated vertex without a loop, a complete graph with all loops present, or a complete unlooped bipartite gra ..."
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Cited by 21 (5 self)
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The problem of counting graph homomorphisms is considered. We show that the counting problem corresponding to a given graph is #Pcomplete unless every connected component of the graph is an isolated vertex without a loop, a complete graph with all loops present, or a complete unlooped bipartite
Corrigendum: The complexity of counting graph homomorphisms
, 2004
"... We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting ..."
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Cited by 3 (0 self)
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We close a gap in the proof of Theorem 4.1 in our paper “The complexity of counting
On counting homomorphisms to directed acyclic graphs
 ICALP (1). Volume 4051 of Lecture Notes in Computer Science
, 2006
"... It is known that if P and NP are different then there is an infinite hierarchy of different complexity classes which lie strictly between them. Thus, if P ≠ NP, it is not possible to classify NP using any finite collection of complexity classes. This situation has led to attempts to identify smaller ..."
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Cited by 28 (4 self)
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for all constraint satisfaction problems. In this paper we give a dichotomy theorem for the problem of counting homomorphisms to directed acyclic graphs. Let H be a fixed directed acyclic graph. The problem is, given an input digraph G, determine how many homomorphisms there are from G to H. We give a
The Complexity of Counting Graph Homomorphisms (Extended Abstract)
"... The problem of counting homomorphisms from a general graph G to a fixed graph H is a natural generalisation of graph colouring, with important applications in statistical physics. The problem of deciding whether any homomorphism exists was considered by Hell and Nesetril. They showed that decision i ..."
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Cited by 4 (0 self)
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The problem of counting homomorphisms from a general graph G to a fixed graph H is a natural generalisation of graph colouring, with important applications in statistical physics. The problem of deciding whether any homomorphism exists was considered by Hell and Nesetril. They showed that decision
Graph Homomorphisms with Complex Values: A Dichotomy Theorem
"... Graph homomorphism problem has been studied intensively. Given an m × m symmetric matrix A, the graph homomorphism function is defined as ZA(G) = Aξ(u),ξ(v), ξ:V →[m] (u,v)∈E where G = (V, E) is any undirected graph. The function ZA(G) can encode many interesting graph properties, including counting ..."
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Cited by 31 (14 self)
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Graph homomorphism problem has been studied intensively. Given an m × m symmetric matrix A, the graph homomorphism function is defined as ZA(G) = Aξ(u),ξ(v), ξ:V →[m] (u,v)∈E where G = (V, E) is any undirected graph. The function ZA(G) can encode many interesting graph properties, including
Counting list homomorphisms and graphs with bounded degrees
, 2003
"... In a series of papers we have classified the complexity of list homomorphism problems.Here we investigate the effect of restricting the degrees of the input graphs. It turns out that the complexity does not change (except when the degree bound is two). We obtain similarresults on restricting the si ..."
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In a series of papers we have classified the complexity of list homomorphism problems.Here we investigate the effect of restricting the degrees of the input graphs. It turns out that the complexity does not change (except when the degree bound is two). We obtain similarresults on restricting
Tight Bounds for Graph Homomorphism and Subgraph Isomorphism
"... We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time V (H)o(V (G)). We also show an exponentialtime reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a possibili ..."
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We prove that unless Exponential Time Hypothesis (ETH) fails, deciding if there is a homomorphism from graph G to graph H cannot be done in time V (H)o(V (G)). We also show an exponentialtime reduction from Graph Homomorphism to Subgraph Isomorphism. This rules out (subject to ETH) a
Exponential time complexity of the permanent and the Tutte polynomial
 in Proceedings of the 37th International Colloquium on Automata, Languages and Programming, ICALP 2010, ser. Lecture Notes in Computer Science
, 2010
"... We show conditional lower bounds for wellstudied #Phard problems: ◦ The number of satisfying assignments of a 2CNF formula with n variables cannot be computed in time exp(o(n)), and the same is true for computing the number of all independent sets in an nvertex graph. ◦ The permanent of an n × n ..."
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Cited by 10 (4 self)
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. Our lower bounds are relative to (variants of) the Exponential Time Hypothesis (ETH), which says that the satisfiability of nvariable 3CNF formulas cannot be decided in time exp(o(n)). We relax this hypothesis by introducing its counting version #ETH, namely that the satisfying assignments cannot
2. A. Bulatov, The Complexity of the Counting Constraint Satisfaction Problem, Electronic Colloquium
"... Graph homomorphisms with complex values: a dichotomy theorem. (English summary) ..."
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Graph homomorphisms with complex values: a dichotomy theorem. (English summary)
Results 1  10
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