Abstract
Abstract The directed vertex leafage of a chordal graph G is the smallest integer k such that G is the intersection graph of subtrees of a rooted directed tree where each subtree has at most k leaves. In this note, we show how to find in time O ( k n ) an optimal colouring, a maximum independent set, a maximum clique, and an optimal clique cover of an n-vertex chordal graph G with directed vertex leafage k if a representation of G is given. In particular, this implies that for any path graph G, the four problems can be solved in time O ( n ) given a path representation of G.
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