Dynamic approach to k-forcing

TL;DR

This paper introduces a dynamic, greedy algorithm to approximate the k-forcing number of graphs, improving existing bounds and solving an open problem in the field.

Contribution

It presents a novel dynamic approach for approximating the k-forcing number, enhancing previous theorems and addressing an open problem.

Findings

The algorithm provides better bounds on the k-forcing number.

It improves upon two existing theorems in the literature.

It successfully answers an open problem related to k-forcing.

Abstract

The k-forcing number of a graph is a generalization of the zero forcing number. In this note, we give a greedy algorithm to approximate the k-forcing number of a graph. Using this dynamic approach, we give corollaries which improve upon two theorems from a recent paper of Amos, Caro, Davila and Pepper [2], while also answering an open problem posed by Meyer [9].