dc.contributor.author Lladó Sánchez, Ana M. dc.contributor.author Miller, Mirka dc.contributor.other Universitat Politècnica de Catalunya. Departament de Matemàtiques dc.date.accessioned 2017-12-20T11:35:12Z dc.date.available 2018-03-01T01:30:36Z dc.date.issued 2017-03 dc.identifier.citation Llado, A., Miller, M. Approximate results for rainbow labelings. "Periodica Mathematica Hungarica", Març 2017, vol. 74, núm. 1, p. 11-21. dc.identifier.issn 0031-5303 dc.identifier.uri http://hdl.handle.net/2117/112321 dc.description The final publication is available at Springer via https://doi.org/10.1007/s10998-016-0151-2] dc.description.abstract A 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.extent 11 p. dc.language.iso eng dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Combinatòria dc.subject Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de nombres dc.subject.lcsh Graph theory dc.subject.lcsh Polynomials dc.subject.other Graph labeling dc.subject.other Polynomial method dc.title Approximate results for rainbow labelings dc.type Article dc.subject.lemac Grafs, Teoria de dc.subject.lemac Polinomis dc.contributor.group Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions dc.identifier.doi 10.1007/s10998-016-0151-2 dc.description.peerreviewed Peer Reviewed dc.subject.ams Classificació AMS::05 Combinatorics::05C Graph theory dc.subject.ams Classificació AMS::11 Number theory::11C Polynomials and matrices dc.relation.publisherversion http://link.springer.com/article/10.1007%2Fs10998-016-0151-2 dc.rights.access Open Access drac.iddocument 19240536 dc.description.version Postprint (author's final draft) upcommons.citation.author Llado, A.; Miller, M. upcommons.citation.published true upcommons.citation.publicationName Periodica Mathematica Hungarica upcommons.citation.volume 74 upcommons.citation.number 1 upcommons.citation.startingPage 11 upcommons.citation.endingPage 21
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