On the acyclic disconnection and the girth
Visualitza/Obre
Cita com:
hdl:2117/86820
Tipus de documentArticle
Data publicació2015-05-11
Condicions d'accésAccés obert
Llevat que s'hi indiqui el contrari, els
continguts d'aquesta obra estan subjectes a la llicència de Creative Commons
:
Reconeixement-NoComercial-SenseObraDerivada 3.0 Espanya
Abstract
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.
CitacióBalbuena, C., Olsen, M. On the acyclic disconnection and the girth. "Discrete applied mathematics", 11 Maig 2015, vol. 186, p. 13-18.
ISSN0166-218X
Versió de l'editorhttp://www.sciencedirect.com/science/article/pii/S0166218X1500027X
Fitxers | Descripció | Mida | Format | Visualitza |
---|---|---|---|---|
On_the_acyclic.pdf | 219,4Kb | Visualitza/Obre |