  In this paper, we deal with the signed bad number and the negative decision
number of graphs. We show that two upper bounds concerning these two parameters
for bipartite graphs in papers [Discrete Math. Algorithms Appl. 1 (2011),
33--41] and [Australas. J. Combin. 41 (2008), 263--272] are not true as they
stand. We correct them by presenting more general bounds for triangle-free
graphs by using the classic theorem of Mantel from the extremal graph theory
and characterize all triangle-free graphs attaining these bounds.
