@article {IOPORT.05644944,
    author       = {Chang, Gerard J. and Lin, Chen-Ying and Tong, Li-Da},
    title        = {Independent arcs of acyclic orientations of complete $r$-partite graphs.},
    year         = {2009},
    journal      = {Discrete Mathematics},
    volume       = {309},
    number       = {13},
    issn         = {0012-365X},
    pages        = {4280-4286},
    publisher    = {Elsevier Science B.V. (North-Holland), Amsterdam},
    doi          = {10.1016/j.disc.2009.01.002},
    abstract     = {Summary: Suppose $D$ is an acyclic orientation of a graph $G$. An arc of $D$ is said to be independent if its reversal results in another acyclic orientation. Let $i(D)$ denote the number of independent arcs in $D$, and let $N(G)=\{i(D):D$ is an acyclic orientation of $G\}$. Also, let $i_{\min}(G)$ be the minimum of $N(G)$ and $i_{\max}(G)$ the maximum. While it is known that $i_{\min}(G)=|V(G)| - 1$ for any connected graph $G$, the present paper determines $i_{\max}(G)$ for complete $r$-partite graphs $G$. We then determine $N(G)$ for any balanced complete $r$-partite graph $G$, showing that $N(G)$ is not a set of consecutive integers. This answers a question raised by West. Finally, we give some complete $r$-partite graphs $G$ whose $N(G)$ is a set of consecutive integers.},
    identifier   = {05644944},
}