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On the acyclic disconnection and the girth
dc.contributor.author | Balbuena Martínez, Maria Camino Teófila |
dc.contributor.author | Olsen, Mika |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental |
dc.date.accessioned | 2016-05-10T08:24:16Z |
dc.date.available | 2017-02-21T01:30:30Z |
dc.date.issued | 2015-05-11 |
dc.identifier.citation | Balbuena, C., Olsen, M. On the acyclic disconnection and the girth. "Discrete applied mathematics", 11 Maig 2015, vol. 186, p. 13-18. |
dc.identifier.issn | 0166-218X |
dc.identifier.uri | http://hdl.handle.net/2117/86820 |
dc.description.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. |
dc.format.extent | 6 p. |
dc.language.iso | eng |
dc.rights.uri | http://creativecommons.org/licenses/by-nc-nd/3.0/es/ |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta |
dc.subject.lcsh | Graph theory |
dc.subject.other | Digraphs |
dc.subject.other | Acyclic disconnection |
dc.subject.other | Girth |
dc.subject.other | Semigirth |
dc.subject.other | Projective planes |
dc.subject.other | Digraphs |
dc.subject.other | Tournaments |
dc.title | On the acyclic disconnection and the girth |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMPTHE - Combinatòria i Teoria Discreta del Potencial pel control de paràmetres en xarxes |
dc.identifier.doi | 10.1016/j.dam.2015.01.025 |
dc.description.peerreviewed | Peer Reviewed |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0166218X1500027X |
dc.rights.access | Open Access |
local.identifier.drac | 15632734 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Balbuena, C.; Olsen, M. |
local.citation.publicationName | Discrete applied mathematics |
local.citation.volume | 186 |
local.citation.startingPage | 13 |
local.citation.endingPage | 18 |
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