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On Partition Dimension of Generalized Convex Polytopes
Journal of Mathematics, 2023 Let G be a graph having no loop or multiple edges, k−order vertex partition for G is represented by γ=γ1,γ2,…,γk. The vector rϕγ=dϕ,γ1,dϕ,γ2,dϕ,γ3⋯,dϕ,γk is the representation of vertex ϕ with respect to γ.
Syed Waqas Shah +5 more
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Distributed Vertex-Cut Partitioning [PDF]
, 2014 Graph processing has become an integral part of big data analytics. With the ever increasing size of the graphs, one needs to partition them into smaller clusters, which can be managed and processed more easily on multiple machines in a distributed fashion. While there exist numerous solutions for edge-cut partitioning of graphs, very little effort has
Rahimian, Fatemeh +3 more
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Tree partitioning via vertex deletion
Electronic Notes in Discrete Mathematics, 2001 Abstract Motivated by tree partitioning problems, we introduce the notion of i-divider of a tree, t -dividers generalize concepts well-known in literature, such as centroids and separators, that are the backbone of tree decomposition algorithms based on vertex deletion.
FINOCCHI, Irene, PETRESCHI, Rossella
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Refined Topological Vertex, Cylindric Partitions and the U(1) Adjoint Theory [PDF]
, 2009 We study the partition function of the compactified 5D U(1) gauge theory (in the Omega-background) with a single adjoint hypermultiplet, calculated using the refined topological vertex.
Aganagic +24 more
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Vertex Set Partitions Preserving Conservativeness
Journal of Combinatorial Theory, Series B, 2000 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ageev, A.A., Kostochka, A.V.
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Topological vertex for 6d SCFTs with ℤ2-twist
Journal of High Energy Physics, 2021 We compute the partition function for 6d N $$ \mathcal{N} $$ = 1 SO(2N) gauge theories compactified on a circle with ℤ2 outer automorphism twist. We perform the computation based on 5-brane webs with two O5-planes using topological vertex with two O5 ...
Hee-Cheol Kim, Minsung Kim, Sung-Soo Kim
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Vertex partitions of chordal graphs [PDF]
Journal of Graph Theory, 2006 AbstractA k‐tree is a chordal graph with no (k + 2)‐clique. An ℓ‐tree‐partition of a graph G is a vertex partition of G into ‘bags,’ such that contracting each bag to a single vertex gives an ℓ‐tree (after deleting loops and replacing parallel edges by a single edge).
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Topological vertex/anti-vertex and supergroup gauge theory
Journal of High Energy Physics, 2020 We propose a new vertex formalism, called anti-refined topological vertex (anti-vertex for short), to compute the generalized topological string amplitude, which gives rise to the supergroup gauge theory partition function.
Taro Kimura, Yuji Sugimoto
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On the b-Domatic Number of Graphs
Discussiones Mathematicae Graph Theory, 2019 A set of vertices S in a graph G = (V, E) is a dominating set if every vertex not in S is adjacent to at least one vertex in S. A domatic partition of graph G is a partition of its vertex-set V into dominating sets. A domatic partition 𝒫 of G is called b-
Benatallah Mohammed +2 more
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Instanton counting and O-vertex
Journal of High Energy Physics, 2021 We present closed-form expressions of unrefined instanton partition functions for gauge groups of type BCD as sums over Young diagrams. For SO(n) gauge groups, we provide a fivebrane web picture of our formula based on the vertex-operator formalism of ...
Satoshi Nawata, Rui-Dong Zhu
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