Packing arc-disjoint triangles in regular and almost regular tournaments
نویسندگان
چکیده
For a tournament T , let ν3(T ) denote the maximum number of pairwise arc-disjoint triangles in T . Let ν3(n) denote the minimum of ν3(T ) ranging over all regular tournaments with n vertices (n odd). It is conjectured that ν3(n) = (1 + on(1))n /9 and proved that n 11.43 (1− on(1)) ≤ ν3(n) ≤ n 9 (1 + on(1)) improving upon the best known upper bound and lower bound. The result is generalized to tournaments where the indegree and outdegree at each vertex may differ by at most βn.
منابع مشابه
Packing Triangles in Regular Tournaments
We prove that a regular tournament with n vertices has more than n 2 11.5 (1 − o(1)) pairwise arc-disjoint directed triangles. On the other hand, we construct regular tournaments with a feedback arc set of size less than n 2 8 , so these tournaments do not have n 8 pairwise arc-disjoint triangles. These improve upon the best known bounds for this problem.
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