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4,771
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
Subgraph Isomorphism in Planar Graphs and Related Problems
, 1999
"... We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used to ..."
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Cited by 153 (3 self)
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We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph into pieces of small treewidth, and applying dynamic programming within each piece. The same methods can be used
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Isomorphic Subgraphs
 Proc. Graph Drawing'99, LNCS 1731
, 1999
"... We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as Geometric Symmetries on the basis of drawings, the other rests upon the graphtheoretical notion of graphs. For a ..."
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Cited by 2 (1 self)
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given graph G the Isomorphic Subgraphs problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G. Hence, G consists of two identical copies and a remainder. There are many NPcomplete or open problems related to our problem, like Graph Isomorphism
Counting subgraphs via homomorphisms
 In Automata, Languages and Programming: ThirtySixth International Colloquium (ICALP
, 2009
"... We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund, ..."
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Cited by 10 (3 self)
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We introduce a generic approach for counting subgraphs in a graph. The main idea is to relate counting subgraphs to counting graph homomorphisms. This approach provides new algorithms and unifies several well known results in algorithms and combinatorics including the recent algorithm of Björklund
Quantum field theory on noncommutative spaces
"... A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommuta ..."
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Cited by 397 (26 self)
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A pedagogical and selfcontained introduction to noncommutative quantum field theory is presented, with emphasis on those properties that are intimately tied to string theory and gravity. Topics covered include the WeylWigner correspondence, noncommutative Feynman diagrams, UV/IR mixing, noncommutative YangMills theory on infinite space and on the torus, Morita equivalences of noncommutative gauge theories, twisted reduced models, and an indepth study of the gauge group of noncommutative YangMills theory. Some of the more mathematical ideas and
Graph homomorphisms: structure and symmetry
"... This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph homomorphisms and mention some results that consider the structure and some parameters of the graphs involved. We ..."
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Cited by 45 (2 self)
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This paper is the first part of an introduction to the subject of graph homomorphism in the mixed form of a course and a survey. We give the basic definitions, examples and uses of graph homomorphisms and mention some results that consider the structure and some parameters of the graphs involved
Tree Depth, Subgraph Coloring and Homomorphism Bounds
, 2004
"... We define the notions tree depth and upper chromatic number of a graph and show their relevance to local  global problems for graphs partitions. Particularly we show that the upper chromatic number coincides with the maximal function which can be locally demanded in a bounded coloring of any pro ..."
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Cited by 6 (0 self)
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We define the notions tree depth and upper chromatic number of a graph and show their relevance to local  global problems for graphs partitions. Particularly we show that the upper chromatic number coincides with the maximal function which can be locally demanded in a bounded coloring of any
Homomorphism Bounded Classes of Graphs
, 2001
"... A class C of graphs is said to be Hbounded if each graph in the class C admits a homomorphism to H. We give a general necessary and sucient condition for the existence of bounds with special local properties. This gives a new proof of HaggkvistHell theorem [5] and implies several cases of the ..."
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A class C of graphs is said to be Hbounded if each graph in the class C admits a homomorphism to H. We give a general necessary and sucient condition for the existence of bounds with special local properties. This gives a new proof of HaggkvistHell theorem [5] and implies several cases
Results 1  10
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4,771