The triangle packing number $ν(G)$ of a graph $G$ is the maximum size of a set of edge-disjoint triangles in $G$. Tuza conjectured that in any graph $G$ there exists a set of at most $2ν(G)$ edges intersecting every triangle in $G$. We show that Tuza's conjecture holds in the random geometric graph for a large range of densities. We also study the problem of covering almost all edges of the random geometric graph with edge-disjoint copies of some fixed graph $F$. In particular, we show the existence of almost-perfect packings for an infinite family of $F$, and state some negative results as well.

翻译：图$G$的三角形打包数$ν(G)$是$G$中边不相交三角形的最大规模。Tuza猜想：对任意图$G$，存在至多$2ν(G)$条边的集合与$G$中每个三角形相交。我们证明在随机几何图中，Tuza猜想对较大范围的密度成立。同时研究了用某个固定图$F$的边不相交复制本覆盖随机几何图几乎所有边的问题。特别地，我们证明了无限族$F$存在几乎完美打包，并给出了部分否定性结果。