179 research outputs found
Long rainbow cycles in proper edge-colorings of complete graphs
We show that any properly edge-colored Kn contains a rainbow cycle with
at least (4=7 − o(1))n edges. This improves the lower bound of n=2 − 1 proved
in [1]
Structure of Colored Complete Graphs Free of Proper Cycles
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
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