Intersection models for weakly chordal graphs? Due to the apparent unpopularity of my previous posts, I'd like to post a question about graph theory which seems to be a popular topic here :)

Among the many known classes of perfect graphs, there are three classes that I find especially interesting:

(1) the weakly chordal graphs, whose obstruction set is $\{C_n,\bar{C_n} : n \geq 5\}$,

(2) the chordal graphs, whose obstruction set is $\{C_n : n \geq 4\}$,

(3) the strongly chordal graphs, whose obstruction set is $\{C_n : n \geq 4\} \cup \{S_n : n \geq 3\}$.

Here, $C_n$ denotes the $n$-cycle, and $S_n$ denotes the $n$-sun (obtained by starting from a cycle $x_1 ... x_n$ and adding the edges $x_i y_i x_{i+1}$ for $1 \leq i \leq n$).

These classes admit polynomial algorithms for clique/independent set, the most general one being for the class of weakly chordal graphs and uses a clever 'two-pair contraction' argument (see 'Optimizing weakly triangulated graphs' by R. Hayward, C.T. Hoang and F. Maffray).

Intersection models are known for classes (2) and (3) as they correspond to the clique graphs of acyclic, resp. totally balanced, hypergraphs. Are there any known results about intersection models for weakly chordal graphs?

As a side note, there is a recursive construction of totally balanced hypergraphs due to Lehel (see 'A characterization of totally balanced matrices'), and I was also wondering about possible algorithmic applications of this result?
If I would like to know something about intersection models, the first reference I would check is the "Topics in Intersection Graph Theory" by McKee and McMorris.  Theorem 1.5 answers your (combinatorial) question.