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The structure of colored complete graphs free of proper cycles
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For a fixed integer m, we consider edge colorings of complete graphs which contain no properly edge colored cycle C m as a subgraph. Within colorings free of these subgraphs, we establish a global structure by bounding the number of colors that can induce a spanning and connected subgraph. In the case of small cycles, namely C 4 , C 5 , and C 6 , we show that our bounds are sharp.
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