  Let $f_{o}(G)$ be the maximum order of an odd induced subgraph of $G$. In
1992, Scott proposed a conjecture that $f_{o}(G)\geq \frac {n} {2\chi(G)}$ for
a graph $G$ of order $n$ without isolated vertices, where $\chi(G)$ is the
chromatic number of $G$. In this paper, we show that the conjecture is not true
for bipartite graphs, but is true for all line graphs. In addition, we also
disprove a conjecture of Berman, Wang and Wargo in 1997, which states that
$f_{o}(G)\geq 2\lfloor\frac {n} {4}\rfloor$ for a connected graph $G$ of order
$n$. Scott's conjecture is open for a graph with chromatic number at least 3.
