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Partitions of Graphs into Cographs
Electronic Notes in Discrete Mathematics, 2002 A cograph is a graph that can be constructed by a single vertex using complementation and disjoint union operations. Equivalently, cographs are exactly those graphs which do not contain an induced path \(P_4\) with four vertices and three edges. The \(c\)-chromatic number \(c(G)\) of a graph \(G\) is the minimum number \(k\) such that the vertex set of
John Gimbel, Jaroslav Nesetril
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The American Mathematical Monthly, 2015 Given a graph $G$ on $n$ vertices, for which $m$ is it possible to partition the edge set of the $m$-fold complete graph $mK_n$ into copies of $G$? We show that there is an integer $m_0$, which we call the \emph{partition modulus of $G$}, such that the set $M(G)$ of values of $m$ for which such a partition exists consists of all but finitely many ...
Sebastian M. Cioaba, Peter J. Cameron
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GAP: Genetic Algorithm Based Large-Scale Graph Partition in Heterogeneous Cluster
IEEE Access, 2020 Graph is an important model to describe various networks, and its scale becomes larger and larger with the development of communication and information technology.
Menghan Li +3 more
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Chromatic partitions of a graph
Discrete Mathematics, 1989 The chromatic partition number \(\chi_ k(G)\) (k\(\geq 1)\) of a graph G is defined to be the minimum number of colours needed in a \(P_ k\)- colouring of G. The following are the main results: (1) For any graph G of order p, \[ \frac{p}{M_ k}\leq \chi_ k(G)\leq \{\frac{p-M_ k}{k}\}+1\quad and\quad -\frac{p}{\beta_ 0k}\leq \chi_ k(G)\leq \{\frac{p ...
E. Sampathkumar 0001 +1 more
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Revisiting the Isoperimetric Graph Partitioning Problem
IEEE Access, 2019 Isoperimetric graph partitioning, which is also known as the Cheeger cut, is NP-hard in its original form. In the literature, multiple modifications to this problem have been proposed to obtain approximation algorithms for clustering applications. In the
Sravan Danda +3 more
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Partitions in Matrices and Graphs
European Journal of Combinatorics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daniel R. Hughes, Navin M. Singhi
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Entropy, 2023 We study partitions (equitable, externally equitable, or other) of graphs that describe physico-chemical systems at the atomic or molecular level; provide examples that show how these partitions are intimately related with symmetries of the systems; and discuss how such a link can further lead to insightful relations with the systems’ physical and ...
Ioannis Michos, Vasilios Raptis
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RBSEP: a reassignment and buffer based streaming edge partitioning approach
Journal of Big Data, 2019 In recent years, the rapid growth of the Internet has led to creation of massively large graphs. Since databases have become very large nowadays, they cannot be processed by a simple machine at an acceptable time anymore; therefore, traditional graph ...
Monireh Taimouri, Hamid Saadatfar
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Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics
Algorithms, 2019 The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article.
Hristo N. Djidjev +4 more
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Design of Heterogeneous Graph Computing System for Large-Scale Dynamic Graph [PDF]
Jisuanji gongchengGraphics Processing Unit (GPU) is not fully utilized when processing large-scale dynamic graphs, and the limitations of GPU-oriented graph partitioning methods lead to performance bottlenecks.
ZHANG Ming, GUO Wenkang, WANG Haifeng
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