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• W1558436568 abstract "Many combinatorial problems can be formulated as can we transform configuration 1 into configuration 2 if certain transformations are allowed? In order to study such questions, we introduce a so-called transformation graph. This graph has the set of all possible configurations as its vertex set, and there is an edge between two configurations if configuration can be obtained from the other by of the allowed transformations. Then a question like can we go from configuration to another one becomes a question about connectivity properties of transformation graphs.In this thesis, we study the following types of transformation graphs in particular:Labelled Token Graphs: Here configurations are arrangements of labelled tokens on a given graph, and we can go from arrangement to another by moving token at a time along an edge of the given graph. We classify all cases when labelled token graphs are connected, and classify all pairs of arrangements that are in the same component. We also look at the problem how hard it is to determine the length of the shortest path between two arrangements.Strong k-Colour Graphs: For this transformation graph, the configurations are the proper vertex-colourings of a given graph with k colours, in which all k colours are actually used. We call such a colouring a strong k-colouring. We study the problem when we can transform any strong k-colouring into any other by recolouring vertex at a time, always maintaining a strong k-colouring. For certain classes of graphs, we can completely determine when the transformation graph of strong k-colourings is connected." @default.
• W1558436568 created "2016-06-24" @default.
• W1558436568 creator A5028801286 @default.
• W1558436568 date "2013-01-01" @default.
• W1558436568 modified "2023-09-23" @default.
• W1558436568 title "Connectivity properties of some transformation graphs" @default.
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