\input zb-basic \input zb-ioport \iteman{io-port 05899036} \itemau{Li, Jinbo; Liu, Guizhen} \itemti{On $f$-edge cover coloring of nearly bipartite graphs.} \itemso{Bull. Malays. Math. Sci. Soc. (2) 34, No. 2, 247-253 (2011).} \itemab Summary: Let $G(V, E)$ be a graph, and let $f$ be an integer function on $V$ with $1\le f(v)\le d(v)$ to each vertex $v\in V$. An $f$-edge cover coloring is an edge coloring $C$ such that each color appears at each vertex $v$ at least $f(u)$ times. The $f$-edge cover chromatic index of $G$, denoted by $\chi_{fc}'(G)$, is the maximum number of colors needed to $f$-edge cover color $G$. It is well-known that $$\min_{v\in V}\,\Biggl\lfloor{d(v)- \mu(v)\over f(v)}\Biggr\rfloor\le \chi_{fc}'(G)\le \delta_f,$$ where $\mu(v)$ is the multiplicity of $v$ and $\delta_f= \min\{\lfloor{d(v)\over f(v)}\rfloor: v\in V(G)\}$. If $\chi_{fc}'= \delta_f$, then $G$ is of $f_c$-class 1, otherwise $G$ is of $f_c$-class 2. In this paper, we give some new sufficient conditions for a nearly bipartite graph to be of $f_c$-class 1. \itemrv{~} \itemcc{} \itemut{nearly bipartite graph; $f$-edge cover coloring; $f$-edge cover chromatic index} \itemli{http://math.usm.my/bulletin/html/vol34\_2\_4.html} \end