Some results related to the tenacity and existence of k-trees

  • Authors:

  • Dara Moazzami;Behzad Salehian

  • Affiliations:

  • University of Tehran, College of Engineering, Department of Engineering Science, P.O.Box: 14395-195, Tehran, Iran;University of Tehran, Department of Mathematics, Tehran, Iran

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

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Abstract

The tenacity of a graph G, T(G), is defined by T(G)=min{|S|+@t(G-S)@w(G-S)}, where the minimum is taken over all vertex cutsets S of V(G), @w(G-S) be the number of components of G-S and @t(G-S) be the number of vertices in the largest component of the graph induced by G-S. A k-tree of a connected graph G is a spanning tree with maximum degree at most k. In this paper we show that if T(G)=@t(G-S)@w(G-S)+1k-2, for any subset S of V(G), with k=3, then G has a k-tree.