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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
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
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
Homomorphism Bounded Classes of Graphs
"... Abstract A class C of graphs is said to be Hbounded if each graph in the class C admitsa homomorphism to H. We give a general necessary and sufficient condition forthe existence of bounds with special local properties. This gives a new proof of H"aggkvistHell theorem [5] and implies sever ..."
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Abstract A class C of graphs is said to be Hbounded if each graph in the class C admitsa homomorphism to H. We give a general necessary and sufficient condition forthe existence of bounds with special local properties. This gives a new proof of H"aggkvistHell theorem [5] and implies
Understanding the Complexity of Induced Subgraph Isomorphisms
"... Abstract. We study lefthand side restrictions of the induced subgraph isomorphism problem: Fixing a class C, for given graphs G ∈ C and arbitrary H we ask for induced subgraphs of H isomorphic to G. For the homomorphism problem this kind of restriction has been studied by Grohe and Dalmau, Kolaitis ..."
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Cited by 8 (1 self)
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Abstract. We study lefthand side restrictions of the induced subgraph isomorphism problem: Fixing a class C, for given graphs G ∈ C and arbitrary H we ask for induced subgraphs of H isomorphic to G. For the homomorphism problem this kind of restriction has been studied by Grohe and Dalmau
Bounded Color Multiplicity Graph Isomorphism is in the #L Hierarchy
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 121 (2004)
, 2004
"... In this paper we study the complexity of Bounded Color Multiplicity Graph Isomorphism BCGIb: the input is a pair of vertexcolored graphs such that the number of vertices of a given color in an input graph is bounded by b. We show that BCGIb is in the #L hierarchy (more precisely, the ModkL hierarch ..."
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Cited by 5 (2 self)
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L hierarchy for some constant k depending on b). Combined with the fact that Bounded Color Multiplicity Graph Isomorphism is logspace manyone hard for every set in the ModkL hierarchy for any constant k, we get a tight classification of the problem using logspacebounded counting classes.
Approximate Graph Isomorphism ⋆
"... Abstract. We study optimization versions of Graph Isomorphism. Given two graphs G1, G2, we are interested in finding a bijection π from V (G1) to V (G2) that maximizes the number of matches (edges mapped to O(log n) edges or nonedges mapped to nonedges). We give an n time approximation scheme that ..."
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Cited by 4 (0 self)
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special case of Graph Isomorphism. Surprisingly, the bounded color class case turns out to be harder than the uncolored case in the approximate setting. 1
Graph Powers and Graph Homomorphisms
, 2010
"... In this paper, we investigate some basic properties of fractional powers. In this regard, we show that for any nonbipartite graph G and positive rational numbers 2q+1. Next, we study the power thickness of G, ..."
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Cited by 1 (0 self)
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In this paper, we investigate some basic properties of fractional powers. In this regard, we show that for any nonbipartite graph G and positive rational numbers 2q+1. Next, we study the power thickness of G,
Graph reconstruction from subgraphs
 DISCRETE MATHEMATICS
, 2001
"... The Reconstruction Conjecture asserts that every finite simple undirected graph on 3 or more vertices is determined, up to isomorphism, by its collection of (unlabeled) onevertexdeleted subgraphs. A more general problem can be investigated if the collection consists of all (unlabeled) subgraphs wi ..."
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Cited by 5 (0 self)
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The Reconstruction Conjecture asserts that every finite simple undirected graph on 3 or more vertices is determined, up to isomorphism, by its collection of (unlabeled) onevertexdeleted subgraphs. A more general problem can be investigated if the collection consists of all (unlabeled) subgraphs
On Recognizing Graphs by Numbers of Homomorphisms
"... Let Hom(G,H) be the number of homomorphisms from a graph G to a graph H. A wellknown result of Lovász states that the function Hom(.,H) from all graphs uniquely determines the graph H upto isomorphism. We study this function restricted to smaller classes of graphs. We show that several natural clas ..."
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Let Hom(G,H) be the number of homomorphisms from a graph G to a graph H. A wellknown result of Lovász states that the function Hom(.,H) from all graphs uniquely determines the graph H upto isomorphism. We study this function restricted to smaller classes of graphs. We show that several natural
Results 1  10
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3,599