The NLC-width and clique-width for powers of graphs of bounded tree-width

  • Authors:

  • Frank Gurski;Egon Wanke

  • Affiliations:

  • Heinrich-Heine-Universität Düsseldorf, Institute of Computer Science, D-40225 Düsseldorf, Germany;Heinrich-Heine-Universität Düsseldorf, Institute of Computer Science, D-40225 Düsseldorf, Germany

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

The k-power graph of a graph G is a graph with the same vertex set as G, in that two vertices are adjacent if and only if, there is a path between them in G of length at most k. A k-tree-power graph is the k-power graph of a tree, a k-leaf-power graph is the subgraph of some k-tree-power graph induced by the leaves of the tree. We show that (1) every k-tree-power graph has NLC-width at most k+2 and clique-width at most k+2+max{@?k2@?-1,0}, (2) every k-leaf-power graph has NLC-width at most k and clique-width at most k+max{@?k2@?-2,0}, and (3) every k-power graph of a graph of tree-width l has NLC-width at most (k+1)^l^+^1-1, and clique-width at most 2@?(k+1)^l^+^1-2.