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- W4298162909 abstract "In a properly edge colored graph, a subgraph using every color at most once is called rainbow. In this thesis, we study rainbow cycles and paths in proper edge colorings of complete graphs, and we prove that in every proper edge coloring of K_n, there is a rainbow path on (3/4-o(1))n vertices, improving on the previously best bound of (2n+1)/3 from Gyarfas and Mhalla. Similarly, a k-rainbow path in a proper edge coloring of K_n is a path using no color more than k times. We prove that in every proper edge coloring of K_n, there is a k-rainbow path on (1-2/(k+1)!)n vertices." @default.
- W4298162909 created "2022-10-01" @default.
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- W4298162909 date "2012-07-03" @default.
- W4298162909 modified "2023-10-17" @default.
- W4298162909 title "On Rainbow Cycles and Paths" @default.
- W4298162909 doi "https://doi.org/10.48550/arxiv.1207.0840" @default.
- W4298162909 hasPublicationYear "2012" @default.
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