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Structure Of Colored Complete Graphs Free Of Proper Cycles, Vincent E. Coll, Colton Magnant, Kathleen Ryan

Department of Mathematical Sciences Faculty Publications

For a fixed integer m, we consider edge colorings of complete graphs which contain no properly edge colored cycle Cm as a subgraph. Within colorings free of these subgraphs, we establish global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of smaller cycles, namely C4,C5, and C6, we show that our bounds are sharp.