Max Independent Set Remains NP-hard when Excluding a Planar Induced Minor

2026-09-10

AI Summary

本文证明了即使排除特定平面图作为诱导子图，最大独立集问题仍为NP难，反驳了相关猜想。

Abstract

We show that there is a fixed planar graph $H$, namely the $5 \times 5$ grid, such that Max Independent Set remains NP-hard in $H$-induced-minor-free graphs. This refutes the Dallard--Milanič--Štorgel conjecture and a weakening of it by Gartland and Lokshtanov, and by Korhonen.

Problem

• Max Independent Set
• NP-hard
• Planar Graph
• Induced Minor

Innovation

• Max Independent Set
• NP-hard
• Planar Graph
• Induced Minor
• 5x5 Grid