A Decomposition of Gallai MultigraphsDiscussiones Mathematicae Graph Theory
AbstractAn 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.
Citation InformationAlexander 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/