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Discrete Optimization, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giovanni Andreatta +3 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Giovanni Andreatta +3 more
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2017
The analysis of large graph plays a prominent role in various fields of research and application area. Initially, we formally define the partitioning scheme based on user needs and requirements. In this paper, we will be dealing with various methods of graph partitioning, its advantages and disadvantages, and from the result we can conclude which is ...
Tanvi Prabhu Dessai +2 more
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The analysis of large graph plays a prominent role in various fields of research and application area. Initially, we formally define the partitioning scheme based on user needs and requirements. In this paper, we will be dealing with various methods of graph partitioning, its advantages and disadvantages, and from the result we can conclude which is ...
Tanvi Prabhu Dessai +2 more
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2003
Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework or cast in a way which is amenable to parallel computation.
Huaijun Qiu, Edwin R. Hancock
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Although inexact graph-matching is a problem of potentially exponential complexity, the problem may be simplified by decomposing the graphs to be matched into smaller subgraphs. If this is done, then the process may cast into a hierarchical framework or cast in a way which is amenable to parallel computation.
Huaijun Qiu, Edwin R. Hancock
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2012
Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, *}-matrix M. Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M-partitions, or M-partitions in ...
Pavol Hell +2 more
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Recently, there has been much interest in studying certain graph partitions that generalize graph colourings and homomorphisms. They are described by a pattern, usually viewed as a symmetric {0, 1, *}-matrix M. Existing results focus on recognition algorithms and characterization theorems for graphs that admit such M-partitions, or M-partitions in ...
Pavol Hell +2 more
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Algorithms for graph partitioning on the planted partition model
Random Structures and Algorithms, 1999Summary: The NP-hard graph bisection problem is to partition the nodes of an undirected graph into two equal-sized groups so as to minimize the number of edges that cross the partition. The more general graph \(\ell\)-partition problem is to partition the nodes of an undirected graph into \(\ell\) equal-size groups so as to minimize the total number of
Anne Condon, Richard M. Karp
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Ars Comb., 1999
Summary: For a given graph \(G\), we fix \(s\), and partition the vertex set into \(s\) classes, so that any given class contains few edges. The result gives a partition \((U_1, \dots , U_s)\), where \(e(U_i) \leq \frac {e(G)}{s^2} + 4e \sqrt {e(G)}\) for each \(1 \leq i \leq s\).
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Summary: For a given graph \(G\), we fix \(s\), and partition the vertex set into \(s\) classes, so that any given class contains few edges. The result gives a partition \((U_1, \dots , U_s)\), where \(e(U_i) \leq \frac {e(G)}{s^2} + 4e \sqrt {e(G)}\) for each \(1 \leq i \leq s\).
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Canadian Mathematical Bulletin, 1968
In 1879 Kempe [5] presented what has become the most famous of all incorrect proofs of the Four Colour Conjecture, but even though his proof was erroneous his method has become quite useful. In 1890 Heawood [4] was able to modify Kempe's method to establish the Five Colour Theorem for planar graphs.
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In 1879 Kempe [5] presented what has become the most famous of all incorrect proofs of the Four Colour Conjecture, but even though his proof was erroneous his method has become quite useful. In 1890 Heawood [4] was able to modify Kempe's method to establish the Five Colour Theorem for planar graphs.
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More Recent Advances in (Hyper)Graph Partitioning
ACM Computing Surveys, 2023Umit V Catalyurek +2 more
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ACM Transactions on Intelligent Systems and Technology, 2021
Shengwei Ji, Chenyang Bu, Xindong Wu
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Shengwei Ji, Chenyang Bu, Xindong Wu
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Graph partitioning models for parallel computing
Parallel Computing, 2000Bruce Hendrickson, Tamara G Kolda
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