We investigate the properties of chordal graphs that follow from the well-known fact that chordal graphs admit tree representations. In particular, we study the structure of reduced clique graphsâ€¦ (More)

Polar graphs are a common generalization of bipartite, cobipartite, and split graphs. They are defined by the existence of a certain partition of vertices, which is NPcomplete to decide for generalâ€¦ (More)

Asteroidal Triple-free (AT-free) graphs have received considerable attention due to their inclusion of various important graphs families, such as interval and cocomparability graphs. The asteroidalâ€¦ (More)

A 2-subcolouring of a graph is a partition of the vertices into two subsets, each inducing a P3-free graph, i.e., a disjoint union of cliques. We give the first polynomial time algorithm to testâ€¦ (More)

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 thisâ€¦ (More)

We introduce a special decomposition, the so-called split-minors, of the reduced clique graphs of chordal graphs. Using this notion, we characterize asteroidal sets in chordal graphs and clique treesâ€¦ (More)