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Approximate results for rainbow labelings
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 |
local.identifier.drac | 19240536 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Llado, A.; Miller, M. |
local.citation.publicationName | Periodica Mathematica Hungarica |
local.citation.volume | 74 |
local.citation.number | 1 |
local.citation.startingPage | 11 |
local.citation.endingPage | 21 |
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