Independent Set on -Free Graphs in Quasi-Polynomial Time

P Gartland, D Lokshtanov - 2020 IEEE 61st Annual Symposium …, 2020 - ieeexplore.ieee.org
We present an algorithm that takes as input a graph G with weights on the vertices, and
computes a maximum weight independent set S of G. If the input graph G excludes a path P …

Induced subgraphs of bounded treewidth and the container method

T Abrishami, M Chudnovsky, M Pilipczuk… - SIAM Journal on …, 2024 - SIAM
A hole in a graph is an induced cycle of length at least 4. A hole is long if its length is at least
5. By, we denote a path on vertices. In this paper, we give polynomial-time algorithms for the …

Sparse induced subgraphs in P6-free graphs

M Chudnovsky, R McCarty, M Pilipczuk… - Proceedings of the 2024 …, 2024 - SIAM
We prove that a number of computational problems that ask for the largest sparse induced
subgraph satisfying some property definable in CMSO2 logic, most notably Feedback Vertex …

A tame vs. feral dichotomy for graph classes excluding an induced minor or induced topological minor

M Milanič, N Pivač - arXiv preprint arXiv:2405.15543, 2024 - arxiv.org
A minimal separator in a graph is an inclusion-minimal set of vertices that separates some
fixed pair of nonadjacent vertices. A graph class is said to be tame if there exists a …

Quasi-Polynomial Time Techniques for Independent Set and Beyond in Hereditary Graph Classes

P Gartland - 2023 - escholarship.org
An independent set in a graph $ G $ is a collection of vertices with no edge between any
two. The {\sc Independent Set} problem is a classic {\sc NP}-Hard problem that takes in a …