Broere, Izak; Chartrand, Gary; Oellermann, Ortrud R.; Wall, Curtiss E. On the edge independence number of a regular graph with large edge connectivity. (English) Zbl 0745.05023 Combinatorial mathematics, Proc. 3rd Int. Conf., New York/ NY (USA) 1985, Ann. N. Y. Acad. Sci. 555, 94-102 (1989). [For the entire collection see Zbl 0699.00014.]Let \(G\) be an \(r\)-regular, \((r-2)\)-edge-connected graph, \(r\geq 3\), of order \(p\) and let \(\ell\) be an integer such that \(0\leq \ell \leq \lfloor {p\over 2}\rfloor\). If \(p\) is even and \(p<2(\ell +1)(r \lfloor {r\over 2}\rfloor + r-1)\), then there are at least \((p-2\ell)/2\) independent edges in \(G\). Similar result for \(p\) odd is given and it is proved that for \(r\geq 4\) the bounds are best possible. Reviewer: P.Horak (Bratislava) Cited in 2 Documents MSC: 05C35 Extremal problems in graph theory 05C40 Connectivity Keywords:edge independence number; regular graph; edge connectivity Citations:Zbl 0699.00014 PDFBibTeX XMLCite \textit{I. Broere} et al., in: A Turanlike neighborhood condition and cliques in graphs. . 94--102 (1989; Zbl 0745.05023)