Absorbent sets and kernels by monochromatic directed paths in m-colored tournaments
نویسندگان
چکیده
In this paper, we consider the following problem due to Erdős: for each m ∈ N, is there a (least) positive integer f(m) so that every finite mcolored tournament contains an absorbent set S by monochromatic directed paths of f(m) vertices? In particular, is f(3) = 3? We prove several bounds for absorbent sets of m-colored tournaments under certain conditions on the number of colors of the arcs incident to every vertex from its in-neighborhood (respectively, ex-neighborhood). In particular, we establish the validity of Erdős’ problem for 3-colored tournaments with this condition. It is also proven that a 3-colored tournament containing no heterochromatic directed triangles with at most bichromatic ex-neighborhoods (respectively, in-neighborhoods) has a kernel by monochromatic directed paths. Previous results are generalized. 198 H. GALEANA-SÁNCHEZ ET AL.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 40 شماره
صفحات -
تاریخ انتشار 2008