Bijections for Cayley trees, spanning trees, and their q-analogues
Journal of Combinatorial Theory Series A
A coding algorithm for Re´nyi trees
Journal of Combinatorial Theory Series A
A partial k-arboretum of graphs with bounded treewidth
Theoretical Computer Science
String coding of trees with locality and heritability
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Evolutionary design of oriented-tree networks using Cayley-type encodings
Information Sciences: an International Journal
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The problem of coding labeled trees has been widely studied in the literature and several bijective codes that realize associations between labeled trees and sequences of labels have been presented. k-trees are one of the most natural and interesting generalizations of trees and there is considerable interest in developing efficient tools to manipulate this class, since many NP-Complete problems have been shown to be polynomially solvable on k-trees and partial k-trees. In 1970 Rényi and Rényi generalized the Prüfer code to a subset of labeled k-trees; subsequently, non redundant codes that realize bijection between k-trees (or Rényi k-trees) and a well defined set of strings were produced. In this paper we introduce a new bijective code for labeled k-trees which, to the best of our knowledge, produces the first encoding and decoding algorithms running in linear time with respect to the size of the k-tree.