On conjectures of Frankl and El‐Zahar
Bernardo Llano, Juan José Montellano‐Ballesteros, Eduardo Rivera‐Campo, Ricardo Strausz · Journal of Graph Theory · 2008
Abstract An induced subgraph ${\cal S}$ of a graph ${\cal G}$ is called a derived subgraph of ${\cal G}$ if ${\cal S}$ contains no isolated vertices. An edge e of ${\cal S}$ is said to be residual if e occurs in more than half of the derived subgraphs of ${\cal S}$ . In this article, we prove that every simple graph with at least one edge contains a non‐residual edge. This was conjectured by El‐Zahar in 1997. © 2008 Wiley Periodicals, Inc. J Graph Theory 57: 344–352, 2008