On four color monochromatic sets with nondecreasing diameter
نویسنده
چکیده
Let m and r be positive integers. Define f(m, r) to be the least positive integer N such that for every coloring of the integers 1, . . . , N with r colors there exist monochromatic subsets B1 and B2 (not necessarily of the same color), each having m elements, such that (a) max(B1)−min(B1) ≤ max(B2)−min(B2), and (b) max(B1) < min(B2). We improve previous upper bounds to determine that f(m, 4) = 12m− 9. ∗Research for this paper was done during the 2000 REU Program held at the University of Idaho under NSF grant DMS9820520, and served as partial fulfillment of the requirements for graduating with departmental honors at Bates College, Lewiston, ME.
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عنوان ژورنال:
- Discrete Mathematics
دوره 290 شماره
صفحات -
تاریخ انتشار 2005