On a Problem of Harary

Paul C. Kainen

doi:10.35834/mjms/1513306832

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Home > Journals > Missouri J. Math. Sci. > Volume 29 > Issue 2 > Article

November 2017 On a Problem of Harary

Paul C. Kainen

Missouri J. Math. Sci. 29(2): 216-218 (November 2017). DOI: 10.35834/mjms/1513306832

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Abstract

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.