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A graph $H$ is said to be {\em light} in a family $\mathfrak{G}$ of graphs ifat least one member of $\mathfrak{G}$ contains a copy of $H$ and there existsan integer $\lambda(H, \mathfrak{G})$ such that each member $G$ of$\mathfrak{G}$ with a copy of $H$ also has a copy $K$ of $H$ such that$\deg_{G}(v) \leq \lambda(H, \mathfrak{G})$ for all $v \in V(K)$. In thispaper, we study the light graphs in the class of graphs with small averagedegree, including the plane graphs with some restrictions on girth.

Light subgraphs in graphs with average degree at most four