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dc.contributor.authorDalfó Simó, Cristina
dc.contributor.authorHuemer, Clemens
dc.contributor.authorSalas Piñon, Julián
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationDalfo, C., Huemer, C., Salas, J. The degree/diameter problem in maximal planar bipartite graphs. "Electronic journal of combinatorics", 2016, vol. 23, núm. 1, p. 1-23.
dc.description.abstractThe (Δ,D)(Δ,D) (degree/diameter) problem consists of finding the largest possible number of vertices nn among all the graphs with maximum degree ΔΔ and diameter DD. We consider the (Δ,D)(Δ,D) problem for maximal planar bipartite graphs, that is, simple planar graphs in which every face is a quadrangle. We obtain that for the (Δ,2)(Δ,2) problem, the number of vertices is n=Δ+2n=Δ+2; and for the (Δ,3)(Δ,3) problem, n=3Δ−1n=3Δ−1 if ΔΔ is odd and n=3Δ−2n=3Δ−2 if ΔΔ is even. Then, we prove that, for the general case of the (Δ,D)(Δ,D) problem, an upper bound on nn is approximately 3(2D+1)(Δ−2)⌊D/2⌋3(2D+1)(Δ−2)⌊D/2⌋, and another one is C(Δ−2)⌊D/2⌋C(Δ−2)⌊D/2⌋ if Δ≥DΔ≥D and CC is a sufficiently large constant. Our upper bounds 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 nn for maximal planar bipartite graphs, which is approximately (Δ−2)k(Δ−2)k if D=2kD=2k, and 3(Δ−3)k3(Δ−3)k if D=2k+1D=2k+1, for ΔΔ and DD sufficiently large in both cases.
dc.format.extent23 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs
dc.subject.lcshGraph theory
dc.subject.otherDegree/diameter Problem
dc.subject.otherPlanar graphs
dc.subject.otherBipartite graphs
dc.titleThe degree/diameter problem in maximal planar bipartite graphs
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.contributor.groupUniversitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
upcommons.citation.authorDalfo, C., Huemer, C., Salas, J.
upcommons.citation.publicationNameElectronic journal of combinatorics

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