科研之友
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摘要
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.
- 出版日期2014
