An algorithm for destroying claws and diamonds

TL;DR

This paper presents an algorithm for the Claw-Diamond-Free Edge Deletion problem, efficiently determining if a graph can be modified by removing at most k edges to eliminate induced claws and diamonds.

Contribution

The paper introduces a new fixed-parameter algorithm with a runtime of O*(3.562^k) for the Claw-Diamond-Free Edge Deletion problem.

Findings

Algorithm runs in O*(3.562^k) time

Efficiently solves the Claw-Diamond-Free Edge Deletion problem

Advances fixed-parameter algorithms for graph modification problems

Abstract

In the {Claw,Diamond}-Free Edge Deletion problem the input is a graph $G$ and an integer $k$, and the goal is to decide whether there is a set of edges of size at most $k$ such that removing the edges of the set from $G$ results a graph that does not contain an induced claw or diamond. In this paper we give an algorithm for this problem whose running time is $O^*(3.562^k)$.