On the unavoidability of oriented trees
Electronic Notes in Theoretical Computer Science(2021)
摘要
A digraph is n-unavoidable if it is contained in every tournament of order n. We first prove that every arborescence of order n with k leaves is (n + k - 1)-unavoidable. We then prove that every oriented tree of order n (n >= 2) with k leaves is (3/2n + 3/2k - 2)-unavoidable and (9/2n - 5/2k - 9/2)unavoidable, and thus (21/8n - 47/16)-unavoidable. Finally, we prove that every oriented tree of order n with k leaves is (n + 144k(2) - 280k + 124)-unavoidable. (C) 2021 Elsevier Inc. All rights reserved.
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关键词
Tournament,Oriented tree,Unavoidable
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