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Vertex colouring edge partitions
Journal of Combinatorial Theory, Series B, 2005 Suppose that the edges of a graph are assigned labels from a \(k\)-set, or equivilently, the edges are partitioned into \(k\) parts. Each vertex \(v\) has an associated multiset \(X_v\) consisting of the labels on its incident edges. The partition is a (proper) vertex coloring if for every edge \(uv\), \(X_u \neq X_v\).
Addario-Berry, L. +3 more
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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).
David R Wood
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Partitions, vertex operator constructions and multi-component KP equations [PDF]
Pacific Journal of Mathematics, 1995 For every partition of a positive integer $n$ in $k$ parts and every point of an infinite Grassmannian we obtain a solution of the $k$ component differential-difference KP hierarchy and a corresponding Baker function. A partition of $n$ also determines a vertex operator construction of the fundamental representations of the infinite matrix algebra $gl_\
Bergvelt, M. J., ten Kroode, A. P. E.
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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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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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Branch and bound with simplicial partitions for global optimization
Mathematical Modelling and Analysis, 2008 Branch and bound methods for global optimization are considered in this paper. Advantages and disadvantages of simplicial partitions for branch and bound are shown.
Julius Žilinskas
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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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Complexity of conditional colouring with given template [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Graph ...
Peter J. Dukes +2 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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On All-loop Integrands of Scattering Amplitudes in Planar N=4 SYM [PDF]
, 2010 We study the relationship between the momentum twistor MHV vertex expansion of planar amplitudes in N=4 super-Yang-Mills and the all-loop generalization of the BCFW recursion relations.
A Brandhuber +35 more
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