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dc.contributor.authorLladó Sánchez, Ana M.
dc.contributor.authorMiller, Mirka
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationLlado, A., Miller, M. Approximate results for rainbow labelings. "Periodica Mathematica Hungarica", Març 2017, vol. 74, núm. 1, p. 11-21.
dc.descriptionThe final publication is available at Springer via]
dc.description.abstractA simple graph G=(V,E) is said to be antimagic if there exists a bijection f:E¿[1,|E|] such that the sum of the values of f on edges incident to a vertex takes different values on distinct vertices. The graph G is distance antimagic if there exists a bijection f:V¿[1,|V|], such that ¿x,y¿V, ¿xi¿N(x)f(xi)¿¿xj¿N(y)f(xj). Using the polynomial method of Alon we prove that there are antimagic injections of any graph G with n vertices and m edges in the interval [1,2n+m-4] and, for trees with k inner vertices, in the interval [1,m+k]. In particular, a tree all of whose inner vertices are adjacent to a leaf is antimagic. This gives a partial positive answer to a conjecture by Hartsfield and Ringel. We also show that there are distance antimagic injections of a graph G with order n and maximum degree ¿ in the interval [1,n+t(n-t)], where t=min{¿,¿n/2¿}, and, for trees with k leaves, in the interval [1,3n-4k]. In particular, all trees with n=2k vertices and no pairs of leaves sharing their neighbour are distance antimagic, a partial solution to a conjecture of Arumugam.
dc.format.extent11 p.
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres
dc.subject.lcshGraph theory
dc.subject.otherGraph labeling
dc.subject.otherPolynomial method
dc.titleApproximate results for rainbow labelings
dc.subject.lemacGrafs, Teoria de
dc.contributor.groupUniversitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::05 Combinatorics::05C Graph theory
dc.subject.amsClassificació AMS::11 Number theory::11C Polynomials and matrices
dc.rights.accessOpen Access
dc.description.versionPostprint (author's final draft)
upcommons.citation.authorLlado, A.; Miller, M.
upcommons.citation.publicationNamePeriodica Mathematica Hungarica

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