graph colouring
Breaking the symmetry of the graph colouring problem with genetic algorithms
... The ability to find quick and robust solutions to hard optimi- sation problems has been appreciated for long time since there are a vast number of practical applications. For example, a timetabling problem can be solved ...
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Topics in graph colouring and graph structures
... of graph colouring traces its origins to 1852, when Francis Guthrie observed that a map of the counties of England can be coloured using four colours in such a way that adjacent counties receive different ...
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Mixed Range-Valued Fuzzy Threshold Graph Colouring T. Jaculin 1, B. Srividhya M. Sc M. Phil2
... We have introduced the new concept of “Range- valued fuzzy threshold graph”. In 1972, Richard carp Introduced dominating set[14] and chavtel and Hammer introduced threshold graph[4]. We combined these two ...
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A grouping hyper heuristic framework: application on graph colouring
... for graph colouring ...solve graph colouring ...for graph colouring, namely Lowest Index Max Crossover (LIMX), Greedy Partition Crossover Lowest In- dex (GPX-LI) and Greedy ...
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Computation of Chromatic Numbers for New Class of Graphs and its Applications
... fractional colouring is applied in the field of optical networks. The graph colouring problem is an optimization problem consists of minimizing the colour ...Fractional colouring determines ...
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A Simple Ant Colony Optimization Algorithm to Select Cluster Heads in Ad Hoc Networks
... suggested graph colouring algorithm is a new ACO-based algorithm; this algorithm can be copied to solve multi-objective optimization problems in cluster formation by defining multi-heuristic functions, ...
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Skewness and Kurtosis on Vertex Colouring of Splitting Graphs
... vertex colouring sum based on a minimum proper colouring of a given Splitting graph S (G ) and we compute the statistical measures Mean, Variance, Median, Standard deviation, Skewness and ...
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Fuzzy Colouring of Interval-Valued Fuzzy Graph
... the colouring of a graph is the most significant component of research in optimization technology and is used for various applications, ...by colouring these graphs. In the usual graph ...
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A Tabu Search based University Lectures Timetable Scheduling Model
... including graph colouring theory based technique, IP/LP method and Constraint Based Satisfaction(s) technique (CPSs); (2) Meta-heuristic approaches also including Case Base Reasoning method (CBR), ...
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Complexity of greedy edge-colouring
... Graph colouring of many graph classes has also been ...line graph of a graph G, denoted L ( G ) , is the graph whose vertices are the edges of G, with ef ∈ E ( L ( G )) whenever ...
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Extending precolourings of circular cliques
... graph where the precoloured components are circular cliques. As the results in the previous section indicate, this general situation is complex. Thus we restrict our attention to two special cases: either q = 1 as ...
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The Complexity of the Empire Colouring Problem
... adjacency graph has no induced subgraph of average degree larger than ...the graph is a for forests of paths of arbitrary lengths (for any r ≥ 2, provided s < 2r − q 2r + 1 4 + 3 2 ...input graph ...
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Textile Application of Natural Colourant from the Roots of Eichhornia crassipes (Mart.) Solms
... its colouring properties on different textile substrates ...red colouring based methods were utilized for colouring of different textile fabric ...good colouring property on wool, nylon and ...
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Colouring of plane graphs with unique maximal colours on faces
... Proof. We proceed by induction on the number of vertices. Let xy ∈ E(G) be an edge of G incident with the outer face and c ∈ {black, blue}. If G has no separating cycles of length two or three, then Lemma 2.1 yields the ...
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Mixing homomorphisms, recolorings, and extending circular precolorings
... to a non-surjective homomorphism g. If g does not map to 0, then we are done as g ∈ S. Otherwise, suppose that g does not map to colour i. Notice that every vertex coloured i + q by g can be recoloured i + q − 1. This ...
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Some Results of Edge Colouring using Families of Disjoint Sets Colouring Technique
... In paper [5] we prove some results in graph theory using colouring of families of disjoint sets technique. We introduced the concept ofset labeled by families of disjoint sets and the degree of this set, as ...
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Visual Analytics for Understanding Spatial Situations from Episodic Movement Data
... Analysis of movement data is now a hot topic in the research areas of machine learning, databases, and visual analytics. However, there are only a few works that address episodic movement data. The use of spatio-temporal ...
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Pointed Conflict-Free Colouring of Digraphs
... a graph with n ...conflict-free colouring with the minimum number of colours for general graphs is ...conflict-free colouring of graphs is studied when every vertex is considered as a member of its ...
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The complexity of the empire colouring problem for linear forests
... Let k and s be positive integers greater than two. In what follows k-SAT denotes the well known (e.g., Garey and Johnson, 1979; Karp, 1972) NP- complete problem of checking the satisfiability of a k-CNF boolean formula. ...
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On clique-colouring of graphs with few P4’s
... Proof If n = q then G is a p-tree, which is 2-clique- colourable by Theorem 8. If n > q then G is either a se- rial graph or a decomposable neighbourhood graph or a p-connected graph. In the first ...
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