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A poset is $(\underline{r}+\underline{s})$ -free if it does not contain two incomparable chains of size r and s, respectively. We prove that when r and s are at least 2, the First-Fit algorithm partitions every $(\underline{r}+\underline{s})$ -free poset P into at most 8(r − 1)(s − 1)w chains, where w is the width of P. This solves an open problem of Bosek et al. (SIAM J Discrete Math 23(4):1992–1999,...
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