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On the Packing Partitioning Problem on Directed Graphs
Mathematics, 2021 This work is aimed to continue studying the packing sets of digraphs via the perspective of partitioning the vertex set of a digraph into packing sets (which can be interpreted as a type of vertex coloring of digraphs) and focused on finding the minimum ...
Babak Samadi, Ismael G. Yero
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AKCE International Journal of Graphs and Combinatorics, 2016 Let G be a graph with chromatic number χ(G) and consider a partition P of G into connected subgraphs. P is a puzzle on G if there is a unique vertex coloring of G using 1, 2, …, χ(G) such that the sums of the numbers assigned to the partition pieces are ...
Daphne Gold +10 more
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Complexity of conditional colouring with given template [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Peter J. Dukes +2 more
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Which metrics for vertex-cut partitioning? [PDF]
2016 11th International Conference for Internet Technology and Secured Transactions (ICITST), 2016 In this paper we focus on vertex-cut graph partitioning and we investigate how it is possible to evaluate the quality of a partition before running the computation. To this purpose we scrutinize a set of metrics proposed in literature. We carry experiments with the widely-used framework for graph processing Apache GraphX and we perform an accurate ...
Mykhailenko, Hlib +2 more
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Acyclic, Star and Oriented Colourings of Graph Subdivisions [PDF]
Discrete Mathematics & Theoretical Computer Science, 2005 Let G be a graph with chromatic number χ(G). A vertex colouring of G is acyclic if each bichromatic subgraph is a forest. A star colouring of G is an acyclic colouring in which each bichromatic subgraph is a star forest. Let χ a (G) and χ s (G)
David R. Wood
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Graphs whose vertex set can be partitioned into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. We give constructions that yield infinite families of graphs that are TI-graphs, as well as constructions that yield ...
Teresa W. Haynes, Michael A. Henning
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Augmenting graphs to partition their vertices into a total dominating set and an independent dominating set [PDF]
Opuscula MathematicaA graph \(G\) whose vertex set can be partitioned into a total dominating set and an independent dominating set is called a TI-graph. There exist infinite families of graphs that are not TI-graphs. We define the TI-augmentation number \(\operatorname{ti}(
Teresa W. Haynes, Michael A. Henning
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Vertex Separators for Partitioning a Graph [PDF]
Sensors, 2008 Finite Element Method (FEM) is a well known technique extensively studiedfor spatial and temporal modeling of environmental processes, weather predictioncomputations, and intelligent signal processing for wireless sensors. The need for hugecomputational power arising in such applications to simulate physical phenomenoncorrectly mandates the use of ...
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Partitions of networks that are robust to vertex permutation dynamics
Special Matrices, 2015 Minimum disconnecting cuts of connected graphs provide fundamental information about the connectivity structure of the graph. Spectral methods are well-known as stable and efficient means of finding good solutions to the balanced minimum cut problem.
Froyland Gary, Kwok Eric
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Towards Yang-Baxter integrability of quantum crystal melting: From Kagome lattice to vertex models
Nuclear Physics B, 2021 This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains.
Thiago Araujo
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