\textsc{Edge Triangle Packing} and \textsc{Edge Triangle Covering} are dual
problems extensively studied in the field of parameterized complexity.
Given a graph G and an integer k, \textsc{Edge Triangle Packing} seeks to
determine whether there exists a set of at least k edge-disjoint triangles in
G,
while \textsc{Edge Triangle Covering} aims to find out whether there exists a
set of at most k edges that intersects all triangles in G.
Previous research has shown that \textsc{Edge Triangle Packing} has a kernel
of (3+ϵ)k vertices, while \textsc{Edge Triangle Covering} has a kernel
of 6k vertices.
In this paper, we show that the two problems allow kernels of 3k vertices,
improving all previous results. A significant contribution of our work is the
utilization of a novel discharging method for analyzing kernel size, which
exhibits potential for analyzing other kernel algorithms