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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.identifier.citationBose, P. [et al.]. Hamiltonicity for convex shape Delaunay and Gabriel graphs. A: European Workshop on Computational Geometry. "35th European Workshop on Computational Geometry (EuroCG 2019): Utrecht, Netherlands: march 18-20, 2019: abstracts". 2019, p. 14:1-14:7.
dc.description.abstractWe study Hamiltonicity for some of the most general variants of Delaunay and Gabriel graphs. Let S be a point set in the plane. The k-order Delaunay graph of S, denoted k-DGC(S), has vertex set S and edge pq provided that there exists some homothet of 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-GGC(S) is defined analogously, except for the fact that the homothets considered are restricted to be smallest homothets of C with p and q on its boundary. We provide upper bounds on the minimum value of k for which k-GGC(S) is Hamiltonian. Since k-GGC(S) ¿ k-DGC(S), all results carry over to k-DGC(S). In particular, we give upper bounds of 24 for every C and 15 for every point-symmetric 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 = 10).
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Equacions diferencials i integrals::Sistemes dinàmics
dc.subject.lcshHamiltonian systems
dc.titleHamiltonicity for convex shape Delaunay and Gabriel graphs
dc.typeConference report
dc.subject.lemacHamilton, Sistemes de
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::37 Dynamical systems and ergodic theory::37K Infinite-dimensional Hamiltonian systems
dc.rights.accessRestricted access - publisher's policy
dc.description.versionPostprint (published version)
local.citation.authorBose, P.; Cano, M.; Saumell, M.; Silveira, R.
local.citation.contributorEuropean Workshop on Computational Geometry
local.citation.publicationName35th European Workshop on Computational Geometry (EuroCG 2019): Utrecht, Netherlands: march 18-20, 2019: abstracts

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