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Título:	Antimagic labelings of caterpillars
Autor/a:	Lozano Bojados, Antoni; Mora Giné, Mercè; Seara Ojea, Carlos
Otros autores:	Universitat Politècnica de Catalunya. Departament de Ciències de la Computació; Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions; Universitat Politècnica de Catalunya. DCG - Discrete and Combinatorial Geometry; Universitat Politècnica de Catalunya. CGA -Computational Geometry and Applications
Abstract:	A k-antimagic labeling of a graph G is an injection from E(G) to {1,2, ..., |E(G)|+k} such that all vertex sums are pairwise distinct, where the vertex sum at vertex u is the sum of the labels assigned to edges incident to u. We call a graph k-antimagic when it has a k-antimagic labeling, and antimagic when it is 0-antimagic. Hartsfield and Ringel conjectured that every simple connected graph other than K2 is antimagic, but the conjecture is still open even for trees. Here we study k-antimagic labelings of caterpillars. We use algorithmic and constructive techniques, instead of the standard Combinatorial NullStellenSatz method, to prove our results: (i) any caterpillar of order n is (⌊(n−1)/2⌋−2)-antimagic; (ii) any caterpillar with a spine of order s with either at least ⌊(3s+1)/2⌋ leaves or ⌊(s−1)/2⌋ consecutive vertices of degree at most 2 at one end of a longest path, is antimagic; and (iii) if p is a prime number, any caterpillar with a spine of order p, p−1 or p−2 is 1-antimagic.
Abstract:	Peer Reviewed
Materia(s):	-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat -Algorithms -Graph theory -Trees (Graph theory) -Antimagic graphs -Labelings -Algorismes -Grafs, Teoria de -Arbres (Teoria de grafs)
Derechos:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Tipo de documento:	Artículo - Versión presentada Artículo
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