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Article
A Decomposition of Gallai Multigraphs
Discussiones Mathematicae Graph Theory
  • Alexander Halperin, Lehigh University
  • Colton Magnant, Georgia Southern University
  • Kyle Pula, University of Denver
Document Type
Article
Publication Date
1-1-2014
DOI
10.7151/dmgt.1740
Disciplines
Abstract
An edge-colored cycle is rainbow if its edges are colored with distinct colors. A Gallai (multi)graph is a simple, complete, edge-colored (multi)graph lacking rainbow triangles. As has been previously shown for Gallai graphs, we show that Gallai multigraphs admit a simple iterative construction. We then use this structure to prove Ramsey-type results within Gallai colorings. Moreover, we show that Gallai multigraphs give rise to a surprising and highly structured decomposition into directed trees.
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This article is under the http://creativecommons.org/licenses/by-nc-nd/3.0/. Article obtained from Discussiones Mathematicae Graph Theory.

Citation Information
Alexander Halperin, Colton Magnant and Kyle Pula. "A Decomposition of Gallai Multigraphs" Discussiones Mathematicae Graph Theory Vol. 34 (2014) p. 331 - 352
Available at: http://works.bepress.com/colton_magnant/44/