Abstract.
There is a great variety of colouring concepts and results in the literature. Here our focus is to survey results on vertex colourings of graphs defined in terms of forbidden induced subgraph conditions. Thus, one who wishes to obtain useful results from a graph coloring formulation of his problem must do more than just show that the problem is equivalent to the general problem of coloring a graph. If there is to be any hope, one must also obtain information about the structure of the graphs that need to be colored (D.S. Johnson [66]).
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Acknowledgments.
We thank Annegret Wagler, Meike Tewes and the anonymous referees for their valuable comments on this text.
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Final version received: September 9, 2003
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Randerath, B., Schiermeyer, I. Vertex Colouring and Forbidden Subgraphs – A Survey. Graphs and Combinatorics 20, 1–40 (2004). https://doi.org/10.1007/s00373-003-0540-1
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DOI: https://doi.org/10.1007/s00373-003-0540-1