Show simple item record

dc.contributor.authorBose, Prosenjit
dc.contributor.authorCano Vila, María del Pilar
dc.contributor.authorSaumell Mendiola, Maria
dc.contributor.authorSilveira, Rodrigo Ignacio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2020-12-21T10:00:49Z
dc.date.available2021-08-01T00:33:51Z
dc.date.issued2020-08
dc.identifier.citationBose, P. [et al.]. Hamiltonicity for convex shape Delaunay and Gabriel graphs. "Computational geometry: theory and applications", Agost 2020, vol. 89, p. 101629:17.
dc.identifier.issn0925-7721
dc.identifier.urihttp://hdl.handle.net/2117/334699
dc.description© 2020. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.description.abstractWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Instead of defining these proximity graphs using circles, we use an arbitrary convex shape \(\mathcal {C}\) . Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k- \({DG}_{\mathcal {C}}(S)\) , has vertex set S and edge pq provided that there exists some homothet of \(\mathcal {C}\) with p and q on its boundary and containing at most k points of S different from p and q. The k-order Gabriel graph k- \({GG}_{\mathcal {C}}(S)\) is defined analogously, except for the fact that the homothets considered are restricted to be smallest homothets of \(\mathcal {C}\) with p and q on its boundary. We provide upper bounds on the minimum value of k for which k- \({GG}_{\mathcal {C}}(S)\) is Hamiltonian. Since k- \({GG}_{\mathcal {C}}(S)\) \(\subseteq \) k- \({DG}_{\mathcal {C}}(S)\) , all results carry over to k- \({DG}_{\mathcal {C}}(S)\) . In particular, we give upper bounds of 24 for every \(\mathcal {C}\) and 15 for every point-symmetric \(\mathcal {C}\) . We also improve the bound to 7 for squares, 11 for regular hexagons, 12 for regular octagons, and 11 for even-sided regular t-gons (for \(t \ge 10)\) . These constitute the first general results on Hamiltonicity for convex shape Delaunay and Gabriel graphs.
dc.description.sponsorshipP.B. was partially supported by NSERC. P.C. was supported by CONACyT. M.S. was supported by the Czech Science Foundation, grant number GJ19-06792Y, and by institutional support RVO:67985807. R.S. was supported by MINECO through the Ram´on y Cajal program. P.C. and R.S. were also supported by projects MINECO MTM2015-63791-R and Gen. Cat. 2017SGR1640. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No 734922.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshHamiltonian systems
dc.subject.otherDelaunay graphs
dc.subject.otherHamiltonicity
dc.subject.otherGabriel graphs
dc.titleHamiltonicity for convex shape Delaunay and Gabriel graphs
dc.typeArticle
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.identifier.doi10.1016/j.comgeo.2020.101629
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37J Finite-dimensional Hamiltonian, Lagrangian, contact, and nonholonomic systems
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S0925772120300237
dc.rights.accessOpen Access
local.identifier.drac28657735
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//MTM2015-63791-R/ES/GRAFOS Y GEOMETRIA: INTERACCIONES Y APLICACIONES/
local.citation.authorBose, P.; Cano, M.; Saumell, M.; Silveira, R.
local.citation.publicationNameComputational geometry: theory and applications
local.citation.volume89
local.citation.startingPage101629:1
local.citation.endingPage101629:17


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record