Extensions of Gallai–Ramsey results

Authors:
Shinya Fujita;Colton Magnant
Affiliations:
Department of Mathematics, Gunma National College of Technology, Maebashi, Gunma 580 Toriba371-8530, Japan;Department of Mathematics, Lehigh University, 14 E. Packer Ave. BethlehemPA, Italy
Venue:
Journal of Graph Theory
Year:
2012

Citing 5
Cited 0

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Abstract

Consider the graph consisting of a triangle with a pendant edge. We describe the structure of rainbow -free edge colorings of a complete graph and provide some corresponding Gallai–Ramsey results. In particular, we extend a result of Gallai to find a partition of the vertices of a rainbow -free colored complete graph with a limited number of colors between the parts. We also extend some Gallai–Ramsey results of Chung and Graham, Faudree et al. and Gyárfás et al. Copyright © 2011 Wiley Periodicals, Inc. J Graph Theory © 2012 Wiley Periodicals, Inc.