A Note on Irreversible 2-Conversion Sets in Subcubic Graphs

Abstract

Irreversible k-conversion set is introduced in connection with the mathematical modeling of the spread of diseases or opinions. We show that the problem to find a minimum irreversible 2-conversion set can be solved in O(n²log ⁶n) time for graphs with maximum degree at most 3 (subcubic graphs) by reducing it to the graphic matroid parity problem, where n is the number of vertices in a graph. This affirmatively settles an open question posed by Kyncl et al. (2014).