Kainen, Paul C. On a problem of Harary. (English) Zbl 1391.05139 Missouri J. Math. Sci. 29, No. 2, 216-218 (2017). Summary: An exercise in [F. Harary, Graph theory. Reading, MA etc.: Addison-Wesley Publishing Company (1969; Zbl 0182.57702), 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. MSC: 05C35 Extremal problems in graph theory 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) Keywords:triangle-free graphs; vertex cover; edge cover; independence number Citations:Zbl 0182.57702 PDF BibTeX XML Cite \textit{P. C. Kainen}, Missouri J. Math. Sci. 29, No. 2, 216--218 (2017; Zbl 1391.05139) Full Text: Euclid OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.