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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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Order, 2008
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Combinatorica, 1993
For even \(n\), let \(p(n)\) denote the number of partitions of \(n\) and \(G(n)\) denote the number of graphical partitions of \(n\). A partition \(\pi=(\lambda_1,\lambda_2,\dots,\lambda_m)\) is graphical if there exists a graph with degree sequence \(\pi\). The authors discuss progress and possible lines in enquiry on the questions of whether or not \
Paul Erdös, L. Bruce Richmond
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For even \(n\), let \(p(n)\) denote the number of partitions of \(n\) and \(G(n)\) denote the number of graphical partitions of \(n\). A partition \(\pi=(\lambda_1,\lambda_2,\dots,\lambda_m)\) is graphical if there exists a graph with degree sequence \(\pi\). The authors discuss progress and possible lines in enquiry on the questions of whether or not \
Paul Erdös, L. Bruce Richmond
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Partitions and the Minimal Excludant
Annals of Combinatorics, 2019G. Andrews, David Newman
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2010
The chapter is structured as follows: I. Interpretative categories I.1 Dividing without partitioning I.2 Applied forms of partitions I.3 The fragility of terminology II. The attractiveness of partition II.1 The interaction of statehood and nationhood II.2 Equality and inequality in partitioning processes II.3 Multiplying states or the attractiveness of
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The chapter is structured as follows: I. Interpretative categories I.1 Dividing without partitioning I.2 Applied forms of partitions I.3 The fragility of terminology II. The attractiveness of partition II.1 The interaction of statehood and nationhood II.2 Equality and inequality in partitioning processes II.3 Multiplying states or the attractiveness of
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Multistage Robust Mixed-Integer Optimization with Adaptive Partitions
Operational Research, 2016D. Bertsimas, Iain Dunning
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