Displaying similar documents to “Counting pattern-free set partitions. II: Noncrossing and other hypergraphs.”

A decomposition of gallai multigraphs

Alexander Halperin, Colton Magnant, Kyle Pula (2014)

Discussiones Mathematicae Graph Theory

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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...