A note on the edge partition of graphs containing either a light edge or an alternating 2-cycle

Xin Zhang, Bei Niu

Let ${\mathcal{G}}_{\alpha }$ be a hereditary graph class (i.e, every subgraph of $G_{\alpha }\in {\mathcal{G}}_{\alpha }$ belongs to ${\mathcal{G}}_{\alpha }$) such that every graph $G_{\alpha }$ in ${\mathcal{G}}_{\alpha }$ has minimu…