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Rapport (Rapport De Recherche) Année : 2018

Polynomial-time Recognition of 4-Steiner Powers

Résumé

The kth-power of a given graph G=(V,E) is obtained from G by adding an edge between every two distinct vertices at a distance at most k in G. We call G a k-Steiner power if it is an induced subgraph of the kth-power of some tree. Our main contribution is a polynomial-time recognition algorithm of 4-Steiner powers, thereby extending the decade-year-old results of (Lin, Kearney and Jiang, ISAAC'00) for k=1,2 and (Chang and Ko, WG'07) for k=3. A graph G is termed k-leaf power if there is some tree T such that: all vertices in V(G) are leaf-nodes of T, and G is an induced subgraph of the kth-power of T. As a byproduct of our main result, we give the first known polynomial-time recognition algorithm for 6-leaf powers.
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Dates et versions

hal-01887266 , version 1 (03-10-2018)
hal-01887266 , version 2 (24-12-2018)

Identifiants

  • HAL Id : hal-01887266 , version 2

Citer

Guillaume Ducoffe. Polynomial-time Recognition of 4-Steiner Powers. [Research Report] University of Bucharest, Faculty of Mathematics and Computer Science; National Institute for Research and Development in Informatics, Romania. 2018. ⟨hal-01887266v2⟩

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