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4,277
Attributed Tree Homomorphism Using Association Graphs
 In Proc. IEEE Int. Conf. on Pattern Recognition
, 2000
"... .... 1 Introduction 2 Tree homomorphisms and maximal cliques 2.1 Notations and definitions Before going into the details of the proposed framework, we need to introduce some graphtheoretical notations and definitions. More details can be found in standard textbooks of graph theory, such as [8]. Le ..."
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Cited by 5 (1 self)
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.... 1 Introduction 2 Tree homomorphisms and maximal cliques 2.1 Notations and definitions Before going into the details of the proposed framework, we need to introduce some graphtheoretical notations and definitions. More details can be found in standard textbooks of graph theory, such as [8
Algebraic Graph Theory
, 2011
"... Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area is the investiga ..."
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Cited by 892 (13 self)
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Algebraic graph theory comprises both the study of algebraic objects arising in connection with graphs, for example, automorphism groups of graphs along with the use of algebraic tools to establish interesting properties of combinatorial objects. One of the oldest themes in the area
Tabu Search  Part I
, 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
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Cited by 680 (11 self)
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, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range
Index Structures for Path Expressions
, 1997
"... In recent years there has been an increased interest in managing data which does not conform to traditional data models, like the relational or object oriented model. The reasons for this nonconformance are diverse. One one hand, data may not conform to such models at the physical level: it may be ..."
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Cited by 333 (7 self)
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be simply specified by a schema which is too complex or changes too often to be described easily as a traditional schema. The term semistructured data has been used to refer to such data. The data model proposed for this kind of data consists of an edgelabeled graph, in which nodes correspond to objects
Matching Hierarchical Structures Using Association Graphs
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453 ..."
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Cited by 212 (24 self)
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this article, please send email to: tpami@computer.org, and reference IEEECS Log Number 108453
Counting graph homomorphisms
 IN:TOPICS IN DISCRETE MATH
, 2006
"... Counting homomorphisms between graphs (often with weights) comes up in a wide variety of areas, including extremal graph theory, properties of graph products, partition functions in statistical physics and property testing of large graphs. In this paper we survey recent developments in the study of ..."
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Cited by 58 (16 self)
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the closeness of (appropriately scaled) homomorphism numbers into the two graphs. We use homomorphism numbers to define convergence of a sequence of graphs, and show that a graph sequence is convergent if and only if it is Cauchy in this distance. Every convergent graph sequence has a limit in the form of a
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 (3 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
Attributed Tree Homomorphism Using
 In Proc. IEEE Int. Conf. on Pattern Recognition
, 2000
"... The matching of hierarchical relational structures is of significant interest in computer vision and pattern recognition. We have recently introduced a new solution to this problem, based on a maximum clique formulation in a (derived) "association graph." This allows us to exploit the full ..."
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framework to handle manytoone correspondences. We define a notion of an # homomorphism (a manytoone mapping) between attributed trees, and provide a method of constructing a weighted association graph where maximal weight cliques are in onetoone correspondence with maximal similarity subtree
Approximate Graph Coloring by Semidefinite Programming.
 In Proceedings of 35th Annual IEEE Symposium on Foundations of Computer Science,
, 1994
"... Abstract. We consider the problem of coloring kcolorable graphs with the fewest possible colors. We present a randomized polynomial time algorithm that colors a 3colorable graph on n vertices with min{O(⌬ 1/3 log 1/2 ⌬ log n), O(n 1/4 log 1/2 n)} colors where ⌬ is the maximum degree of any vertex ..."
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Cited by 210 (7 self)
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vertex. Besides giving the best known approximation ratio in terms of n, this marks the first nontrivial approximation result as a function of the maximum degree ⌬. This result can be generalized to kcolorable graphs to obtain a coloring using min{O(⌬ 1Ϫ2/k log 1/2 ⌬ log n), O(n 1Ϫ3/(kϩ1) log 1/2 n
Graph minors. X. Obstructions to treedecomposition
 J. COMB. THEORY, SERIES B
, 1991
"... Roughly, a graph has small “treewidth” if it can be constructed by piecing small graphs together in a tree structure. Here we study the obstructions to the existence of such a tree structure. We find, for instance: (i) a minimax formula relating treewidth with the largest such obstructions (ii) an ..."
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Cited by 207 (10 self)
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) an association between such obstructions and large grid minors of the graph (iii) a “treedecomposition” of the graph into pieces corresponding with the obstructions. These results will be of use in later papers.
Results 1  10
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