The Binding Number of k-Trees

The notion of k -trees for k ≥ 2 has been introduced by Harary and Palmer [2]. This notion is a natural generalization of an ordinary tree (1-tree). The binding number was introduced by Woodall [6]. Kane, Mohanty and Straus [3] have proved general results about realizing sets for the binding number in the case if the binding number is less than or equal 1. Farago [1] has proved that the problem of calculating the binding number in that case is polynomially solvable. We shall establish some special properties of realizing sets for the binding number of k -trees in the case if bind (G)