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dc.contributor.authorÁbrego, Bernardo M.
dc.contributor.authorFernández Merchant, Silvia
dc.contributor.authorKano, Mikio
dc.contributor.authorOrden, David
dc.contributor.authorPérez Lantero, Pablo
dc.contributor.authorSeara Ojea, Carlos
dc.contributor.authorTejel Altarriba, Francisco Javier
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationÁbrego, B. [et al.]. K-1,K-3-covering red and blue points in the plane. "Discrete mathematics and theoretical computer science", 31 Gener 2019, vol. 21, núm. 3, p. 1-29.
dc.description.abstractWe say that a finite set of red and blue points in the plane in general position can be K1,3-covered if the set can be partitioned into subsets of size 4, with 3 points of one color and 1 point of the other color, in such a way that, if at each subset the fourth point is connected by straight-line segments to the same-colored points, then the resulting set of all segments has no crossings. We consider the following problem: Given a set R of r red points and a set B of b blue points in the plane in general position, how many points of R ¿ B can be K1,3-covered? and we prove the following results: (1) If r = 3g + h and b = 3h + g, for some non-negative integers g and h, then there are point sets R ¿ B, like {1, 3}-equitable sets (i.e., r = 3b or b = 3r) and linearly separable sets, that can be K1,3-covered. (2) If r = 3g + h, b = 3h + g and the points in R ¿ B are in convex position, then at least r + b - 4 points can be K1,3-covered, and this bound is tight. (3) There are arbitrarily large point sets R ¿ B in general position, with r = b + 1, such that at most r + b - 5 points can be K1,3-covered. (4) If b = r = 3b, then at least 8 9 (r + b - 8) points of R ¿ B can be K1,3-covered. For r > 3b, there are too many red points and at least r - 3b of them will remain uncovered in any K1,3-covering.
dc.format.extent29 p.
dc.publisherChapman & Hall/CRC
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències
dc.subject.lcshComputer science--Mathematics
dc.subject.otherNon-crossing geometric graph
dc.subject.otherred and blue points
dc.titleK-1,K-3-covering red and blue points in the plane
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::68 Computer science::68R Discrete mathematics in relation to computer science
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/H2020/734922/EU/Combinatorics of Networks and Computation/CONNECT
local.citation.authorÁbrego, B.; Fernández, S.; Kano, M.; Orden, D.; Perez-Lantero, P.; Seara, C.; Tejel, F.
local.citation.publicationNameDiscrete mathematics and theoretical computer science

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