Number of maximal cliques in a ($2C_4$, $C_5$, $P_5$)-free graph So far, I have found out that chordal graphs have linear number of maximal cliques with respect to the number of vertices.
In general case, it is exponential.
I am trying to determine whether the number of maximal cliques in a $(2C_4, C_5,P_5)$-free graph with respect to the number of vertices.
In a $(2C_4, C_5,P_5)$-free graph, the largest induced cycle is of length 4, and no two induced 4-cycles are edge-disjoint.
Is there a paper that mentions such result?
The famous graph (the complement of the disjoint union of $n/3$ triangles) with $3^{n/3}$ maximal cliques is $K_1 \cup K_2$-free, and thus has none of $2C_4$, $C_5$, $P_5$ as an induced subgraph.
https://doi.org/10.1007/BF02760024