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We study online fractional vertex cover on forests under edge arrival. We give a deterministic algorithm with competitive ratio at most 4 - √5 ≈ 1.764, which simultaneously produces an online fractional matching with competitive ratio of at least 1/(4 - √5) ≈ 0.566. This improves on the previous best competitive ratios of 11/6 ≈ 1.833 and 5/9 ≈ 0.555, respectively.
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Marcin Bieńkowski (2026) studied this question.
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