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The degree/diameter problem in maximal planar bipartite graphs
dc.contributor.author | Dalfó Simó, Cristina |
dc.contributor.author | Huemer, Clemens |
dc.contributor.author | Salas Piñon, Julián |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.date.accessioned | 2015-02-20T12:42:33Z |
dc.date.available | 2015-02-20T12:42:33Z |
dc.date.created | 2014 |
dc.date.issued | 2014 |
dc.identifier.citation | Dalfo, C.; Huemer, C.; Salas, J. The degree/diameter problem in maximal planar bipartite graphs. "Electronic notes in discrete mathematics", 2014, vol. 46, p. 73-80. |
dc.identifier.issn | 1571-0653 |
dc.identifier.uri | http://hdl.handle.net/2117/26448 |
dc.description.abstract | The (¿;D) (degree/diameter) problem consists of nding the largest possible number of vertices n among all the graphs with maximum degree ¿ and diameter D. We consider the (¿;D) problem for maximal planar bipartite graphs, that are simple planar graphs in which every face is a quadrangle. We obtain that for the (¿; 2) problem, the number of vertices is n = ¿+2; and for the (¿; 3) problem, n = 3¿¿1 if ¿ is odd and n = 3¿ ¿ 2 if ¿ is even. Then, we study the general case (¿;D) and obtain that an upper bound on n is approximately 3(2D + 1)(¿ ¿ 2)¿D=2¿ and another one is C(¿ ¿ 2)¿D=2¿ if ¿ D and C is a sufficiently large constant. Our upper bound improve for our kind of graphs the one given by Fellows, Hell and Seyffarth for general planar graphs. We also give a lower bound on n for maximal planar bipartite graphs, which is approximately (¿ ¿ 2)k if D = 2k, and 3(¿ ¿ 3)k if D = 2k + 1, for ¿ and D sufficiently large in both cases. |
dc.format.extent | 8 p. |
dc.language.iso | eng |
dc.rights | Attribution-NonCommercial-NoDerivs 3.0 Spain |
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::Teoria de grafs |
dc.subject.lcsh | Graph theory |
dc.subject.other | (¿,D) problem |
dc.subject.other | maximal planar bipartite graphs |
dc.title | The degree/diameter problem in maximal planar bipartite graphs |
dc.type | Article |
dc.subject.lemac | Grafs, Teoria de |
dc.contributor.group | Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.rights.access | Open Access |
local.identifier.drac | 15340934 |
dc.description.version | Postprint (published version) |
local.citation.author | Dalfo, C.; Huemer, C.; Salas, J. |
local.citation.publicationName | Electronic notes in discrete mathematics |
local.citation.volume | 46 |
local.citation.startingPage | 73 |
local.citation.endingPage | 80 |
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