Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903583 | European Journal of Combinatorics | 2018 | 6 Pages |
Abstract
In 1995, Stiebitz asked the following question: For any positive integers s,t, is there a finite integer f(s,t) such that every digraph D with minimum out-degree at least f(s,t) admits a bipartition (A,B) such that A induces a subdigraph with minimum out-degree at least s and B induces a subdigraph with minimum out-degree at least t? We give an affirmative answer for tournaments, multipartite tournaments, and digraphs with bounded maximum in-degrees. In particular, we show that for every ϵ with 0<ϵ<1â2, there exists an integer δ0 such that every tournament with minimum out-degree at least δ0 admits a bisection (A,B), so that each vertex has at least (1â2âϵ) of its out-neighbors in A, and in B as well.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Donglei Yang, Yandong Bai, Guanghui Wang, Jianliang Wu,