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For a vertex $v$ and a multi-set $\\mathcal{F}$ of graphs, the suspension $\\mathcal{F}+v$ of $\\mathcal{F}$ is the graph obtained by connecting the vertex $v$ to all vertices of $F$ for each $F\\in \\mathcal{F}$. For two integers $k\\ge1$ and $r\\ge2$, let $H_i$ be a graph containing a critical edge with chromatic number $r$ for any $i\\in\\{1,\\ldots,k\\}$, and let $H=\\{H_1,\\ldots,H_k\\}+v$. 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