NP-Hardness of the $H$-Free Edge-Deletion Problem

2026-09-09

AI Summary

本文证明了对于包含环的任意图H，H-自由边删除问题是NP难的，从而解决了Gishboliner等人提出的猜想。

Abstract

For a graph $H$, the $H$-freeness edge-deletion problem is the algorithmic problem of finding, for an input graph $G$, the minimum number of edges of $G$ whose deletion turns $G$ into an $H$-free graph. We show that for every graph $H$ containing a cycle, this problem is NP-hard. This proves a conjecture of Gishboliner, Levanzov and Shapira, and completes the characterization of the complexity of the $H$-freeness edge-deletion problem, answering a question of Alon, Shapira and Sudakov.

Problem

• NP-hard
• H-free
• edge-deletion

Innovation

• NP-hardness
• H-free edge-deletion problem
• graph theory