Anti-van der Waerden Numbers of 3-Term Arithmetic Progression
نویسندگان
چکیده
The anti-van der Waerden number, denoted by aw([n], k), is the smallest r such that every exact r-coloring of [n] contains a rainbow k-term arithmetic progression. Butler et al. showed that dlog3 ne + 2 6 aw([n], 3) 6 dlog2 ne + 1, and conjectured that there exists a constant C such that aw([n], 3) 6 dlog3 ne + C. In this paper, we show this conjecture is true by determining aw([n], 3) for all n. We prove that for 7 · 3m−2 + 1 6 n 6 21 · 3m−2, aw([n], 3) = { m + 2, if n = 3m m + 3, otherwise.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 24 شماره
صفحات -
تاریخ انتشار 2017