Graphs with polynomially many minimal separators

Citation:

T. Abrishami, M. Chudnovsky, C. Dibek, S. Thomassé, N. Trotignon, and K. Vušković, “Graphs with polynomially many minimal separators,” Journal of Combinatorial Theory, Series B, vol. 152, pp. 248-280, 2022.

Abstract:

We show that graphs that do not contain a theta, pyramid, prism, or turtle as an induced subgraph have polynomially many minimal separators. This result is the best possible in the sense that there are graphs with exponentially many minimal separators if only three of the four induced subgraphs are excluded. As a consequence, there is a polynomial time algorithm to solve the maximum weight independent set problem for the class of (theta, pyramid, prism, turtle)-free graphs. Since every prism, theta, and turtle contains an even hole, this also implies a polynomial time algorithm to solve the maximum weight independent set problem for the class of (pyramid, even hole)-free graphs.

[arXiv]

Last updated on 10/21/2021