A Note on the Feedback Arc Set Problem and Acyclic Subdigraphs in Bipartite Tournaments
2017 ◽
Vol 17
(03n04)
◽
pp. 1741004
Keyword(s):
Given a digraph D a feedback arc set is a subset X of the arcs of D such that D − X is acyclic. Let β(D) denote de minimum cardinality of a feedback arc set of D. In this paper we prove that a bipartite tournament T with minimum out-degree at least r satisfies β(T) ≥ r2. A lower bound and an upper bound for β(T) are given in terms of the bipartite dichromatic number. We define the bipartite dichromatic number of a balanced bipartite tournament Tn,n and use this invariant to give an upper bound for the minimum cardinality of a feedback arc set of Tn,n. We also prove that for each positive integer k ≥ 3 there is an integer N(k) such that if n ≥ N(k), then each balanced bipartite tournament contains an acyclic bipartite tournament Tk,k.
1991 ◽
Vol 34
(1)
◽
pp. 121-142
◽
Keyword(s):
Keyword(s):
2021 ◽
Vol 14
(1)
◽
pp. 314-326
Keyword(s):
1998 ◽
Vol 58
(1)
◽
pp. 1-13
◽
Keyword(s):
Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
2016 ◽
Vol 26
(12)
◽
pp. 1650204
◽
Keyword(s):