Gallai's Path Decomposition for 2-degenerate Graphs

Gallai's path decomposition conjecture states that if $G$ is a connected graph on $n$ vertices, then the edges of can be decomposed into at most $\lceil \frac{n }{2} \rceil$ paths. A said to an odd semi-clique it obtained from clique $2k+1$ vertices by deleting $k-1$ edges. Bonamy and Perrett asked every $\lfloor \frac{n}{2} \rfloor$ paths unless semi-clique. 2-degenerate subgraph has vertex degree $2$. In this paper, we prove any triangle.