On circuits through five edges
\textit{L. Lovász} [Problem 5, Period. Math. Hung. 4, 82 (1974)] and \textit{D. R. Woodall} [J. Comb. Theory, Ser. B 22, 274-278 (1977; Zbl 0362.05069)] independently conjectured that if \(L\) is an independent set of \(k\) vertices in a \(k\)-connected graph \(G\), then \(G\) has a circuit containing the edges of \(L\) iff \(L\) is not an odd edge cut. Lovász [op. cit.] proved the conjecture true for \(k=3\) while the case \(k=4\) was settled affirmatively, independently, by Robertson (unpublished manuscript), \textit{P. L. Erdös} and \textit{E. Györi} [Acta Math. Hung. 46, 311-313 (1985; Zbl 0588.05024)], and \textit{M. V. Lomonosov} [Cycles through prescribed elements in a graph, Paths, flows, and VLSI-layout, Proc. Meet., Bonn/Ger. 1988, Algorithms Comb. 9, 215-234 (1990; Zbl 0751.05059)]. The author shows the conjecture is true for the case \(k=5\).
scientific article; zbMATH DE number 955094