Open Access
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


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.


Download Citation

Paul C. Kainen. "On a Problem of Harary." Missouri J. Math. Sci. 29 (2) 216 - 218, November 2017.


Published: November 2017
First available in Project Euclid: 15 December 2017

zbMATH: 06905066
MathSciNet: MR3737298
Digital Object Identifier: 10.35834/mjms/1513306832

Primary: 05C35

Keywords: edge cover , independence number , triangle-free graphs , vertex cover

Rights: Copyright © 2017 Central Missouri State University, Department of Mathematics and Computer Science

Vol.29 • No. 2 • November 2017
Back to Top