An exercise in Harary [1, p. 100] states that the product of the vertex independence number and the vertex covering number is an upper bound on the number of edges in a bipartite graph. In this note, we extend the bound to triangle-free graphs, and show that equality holds if and only if the graph is complete bipartite.
"On a Problem of Harary." Missouri J. Math. Sci. 29 (2) 216 - 218, November 2017. https://doi.org/10.35834/mjms/1513306832