
Planar graphs have bounded nonrepetitive chromatic number
A colouring of a graph is "nonrepetitive" if for every path of even orde...
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Colouring graphs with no induced sixvertex path or diamond
The diamond is the graph obtained by removing an edge from the complete ...
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Reconfiguration Graph for Vertex Colourings of Weakly Chordal Graphs
The reconfiguration graph R_k(G) of the kcolourings of a graph G contai...
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Shifting paths to avoidable ones
An extension of an induced path P in a graph G is an induced path P' suc...
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Path matrix and path energy of graphs
Given a graph G, we associate a path matrix P whose (i, j) entry represe...
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An application of the Gyárfás path argument
We adapt the Gyárfás path argument to prove that t2 cops can capture a ...
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Notes on Tree and Pathchromatic Number
Treechromatic number is a chromatic version of treewidth, where the cos...
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Nonrepetitive graph colouring
A vertex colouring of a graph G is "nonrepetitive" if G contains no path for which the first half of the path is assigned the same sequence of colours as the second half. Thue's famous theorem says that every path is nonrepetitively 3colourable. This paper surveys results about nonrepetitive colourings of graphs. The goal is to give a unified and comprehensive presentation of the major results and proof methods, as well as to highlight numerous open problems.
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