The edge-coloring problem and related problems
Complexity of clique coloring and related problems
... clique coloring can be a very different problem from ordinary vertex ...clique coloring is not a hereditary property: it is possible that a graph is k-clique-colorable, but it has an induced subgraph ...
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COLORING PROBLEMS
... a coloring witnessing a positive answer to Question ...a problem originally published in the Hungarian journal K¨ oMaL (K¨ oz´ episkolai Matematikai ´ es Fizikai Lapok), a Mathematics and Physics journal ...
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Edge-Coloring and f-Coloring for Various Classes of Graphs
... An edge-coloring of a graph G is to color all the edges of G so that no two adjacent edges are colored with the same ...an edge-coloring is called the chromatic index of G and denoted by χ 0 ...
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On the edge coloring of graph products
... Also, Anderson and Lipman posed the question about the edge chromatic number of GρP 2 when G is of class 2 and hinted that this would be a di ffi cult problem. Jaradat gave a complete answer for this question ...
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Cost Edge Coloring of a Cactus
... Cost Edge-Coloring, Minimum Cost Maximum Flow Problem ...and edge set E, and let C be a set of colors. An edge-coloring of G is to color all the edges in E so that any two ...
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Time complexity analysis of RLS and (1 + 1) EA for the edge coloring problem
... • Augmenting paths that are blocked can become unblocked, which may suddenly and drastically increase the length of the shortest augmenting path. It seems plausible that search points with many conlicts have many ...
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On Split-Coloring Problems
... split-coloring problem consists in minimizing the number of split graphs which cover all the vertices of ...this problem does not seem to have been studied to our ...only coloring ...
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3-consecutive edge coloring of a graph
... Proof. If G consists of more than one component, each of them contains some edges and hence, ψ ′ 3c ( G ) > 1. Otherwise, due to Theorem 2 , ψ 3c ′ ( G ) ≥ 2 if and only if the graph has a stable cutset. We will see ...
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List-coloring and sum-list-coloring problems on graphs
... question of how many colors are needed to create an f -assignment for a graph G that shows f is not a choice function for G. How does this number relate to certain parameters of the graph? As we showed that paths of ...
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Parameterized pre-coloring extension and list coloring problems
... List Coloring and Pre-Coloring Extension ...List Coloring, and hence also Pre-Coloring Extension, parameterized by the size of a clique modulator admits a randomized FPT algorithm with a ...
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Coloring and covering problems on graphs
... We show that each such ordering separates the fraction 2m+1 6m of the T-pairs. This fraction is smaller than m+1 3m . Hence this strategy shows that the separation game has value at least 2m+1 6m . By making the T-pairs ...
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Coloring and Labeling Problems on Graphs
... the problem to choosing two colors for each edge on a collection of vertex-disjoint cycles; each edge of these cycles has either 3, 4, or 5 remaining colors ...available. Coloring a graph from ...
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Coloring problems in graph theory
... graph coloring was introduced in order to solve the problem of coloring countries on a map so that no two countries that shared a border received the same ...graph coloring, known as a proper ...
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Coloring problems in graph theory
... PACKING COLORING ON INFINITE LATTICES ...is related to its frequency, so the distance a pair of towers broadcasting the same frequency must be apart is related to the frequency of the ...broadcast ...
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Streaming and Massively Parallel Algorithms for Edge Coloring
... 2 Noga Alon, László Babai, and Alon Itai. A Fast and Simple Randomized Parallel Algorithm for the Maximal Independent Set Problem. J. Algorithms, 7(4):567–583, December 1986. doi:10.1016/0196-6774(86)90019-2. 3 ...
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Open Distance Pattern Edge Coloring of a Graph
... Color Problem in 1852, research on graph colorings has developed [4] into one of the most popular areas of graph ...graph coloring involved in finding the minimum number of colors to be assigned to the ...
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When the vertex coloring of a graph is an edge coloring of its line graph - a rare coincidence
... an edge coloring is proper if and only if every three consecutive edges are colored properly; whilst it is a 3-consecutive edge coloring if and only if no three consecutive edges are colored ...
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Exact Algorithms for the Graph Coloring Problem
... Master Problem represents a fractional color- ing, then there are two vertices u, v ∈ V (G) such that, without loss of generality, u ∈ S 1 ∩ S 2 and v ∈ S 1 \ S 2 ...an edge between ...
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An exact algorithm for the Partition Coloring Problem
... 1.2. Paper Contribution In Section 2 we introduce a new formulation for the PCP with an exponential number of variables and in Section 3 we design a Brach-and-Price algorithm to solve it to proven optimality. Based on a ...
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Quantum annealing of the graph coloring problem
... MACOL and Evo-Div both use Tabu as the underlying local search, and a way has been found to fix its parameters and still obtain acceptable performance for a wide variety of graphs. Therefore, standard versions of these ...
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