On a problem of Harary. (English) Zbl 1391.05139

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.


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.)


Zbl 0182.57702
Full Text: Euclid


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