TY - MGZN
AU - Balbuena, C.
AU - Olsen, M.
T2 - Discrete applied mathematics
Y1 - 2015
VL - 186
SP - 13
EP - 18
DO - 10.1016/j.dam.2015.01.025
UR - http://www.sciencedirect.com/science/article/pii/S0166218X1500027X
AB - The acyclic disconnection, (omega) over right arrow (D), of a digraph D is the maximum number of connected components of the underlying graph of D - A(D*), where D* is an acyclic subdigraph of D. We prove that (omega) over right arrow (D) >= g - 1 for every strongly connected digraph with girth g >= 4, and we show that (omega) over right arrow (D) = g - 1 if and only if D congruent to C-g for g >= 5. We also characterize the digraphs that satisfy (omega) over right arrow (D) = g - 1, for g = 4 in certain classes of digraphs. Finally, we define a family of bipartite tournaments based on projective planes and we prove that their acyclic disconnection is equal to 3. Then, these bipartite tournaments are counterexamples of the conjecture (omega) over right arrow (T) = 3 if and only if T congruent to (C) over right arrow (4) posed for bipartite tournaments by Figueroa et al. (2012). (C) 2015 Elsevier B.V. All rights reserved.
TI - On the acyclic disconnection and the girth
ER -