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Disconnected Colors in Generalized Gallai-Colorings
Journal of Graph Theory
  • Shinya Fujita, Maebashi Institute of Technology
  • András Gyárfás, Hungarian Academy of Sciences
  • Colton Magnant, Georgia Southern University
  • Ákos Seress, Ohio State University - Main Campus
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Gallai-colorings of complete graphs—edge colorings such that no triangle is colored with three distinct colors—occur in various contexts such as the theory of partially ordered sets (in Gallai's original paper), information theory and the theory of perfect graphs. A basic property of Gallai-colorings with at least three colors is that at least one of the color classes must span a disconnected graph. We are interested here in whether this or a similar property remains true if we consider colorings that do not contain a rainbow copy of a fixed graph F. We show that such graphs F are very close to bipartite graphs, namely, they can be made bipartite by the removal of at most one edge. We also extend Gallai's property for two infinite families and show that it also holds when F is a path with at most six vertices.

Citation Information
Shinya Fujita, András Gyárfás, Colton Magnant and Ákos Seress. "Disconnected Colors in Generalized Gallai-Colorings" Journal of Graph Theory Vol. 74 Iss. 1 (2013) p. 104 - 114 ISSN: 1097-0118
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