Randomly perturbed digraphs with n-edge-colorings contain rainbow copies of all oriented cycles of all lengths simultaneously, with high probability.
Long paths and Hamiltonicity in random graphs
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abstract
We discuss several classical results about long paths and Hamilton cycles in random graphs and present accessible versions of their proofs, relying on the Depth First Search (DFS) algorithm and the notion of boosters.
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math.CO 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
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Universality for rainbow oriented cycles in perturbed digraphs
Randomly perturbed digraphs with n-edge-colorings contain rainbow copies of all oriented cycles of all lengths simultaneously, with high probability.