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Not every graph has a robust cycle basis.
by
Richard H. Hammack
Virginia Commonwealth University
Robust cycle bases of graphs have both theoretical and biological applications. However, robust cycle bases are known to exist only for a few classes of graphs. Despite this, previously no graph was known to not have a robust cycle basis. Theorem. The complete bipartite graphs Kn, n have no robust cycle basis when n ≥ 8. Open questions, including the gap 5 ≤ n ≤ 7, and for other graphs are described. This is joint work with Paul Kainen.
Date received: April 19, 2017
Copyright © 2017 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbof-19.