Size and spectral conditions for a graph with given minimum degree to be $k$-$d$-critical

Zhenhao Zhang, Xiaogang Liu, Ligong Wang

A $k$-matching in a graph $G$ is defined as a function $f:E(G)\to \{0,1,\dots ,k\}$ satisfying ${\sum }_{e\in E_G(v)}f(e)$ $\le k$ for each vertex $v\in V(G)$, where $E_G(v…