Independent cycles with limited size in a graph
The following generalization of a result of \textit{K. Corrádi} and \textit{A. Hajnal} [Acta Math. Acad. Sci. Hung. 14, 423-439 (1963; Zbl 0118.190)] is proved. Let \(k\) and \(s\) be two positive integers with \(s\geq 3\). Let \(G\) be a graph of order \(n\geq sk\) and define \(q\) and \(r\) by \(n= qk+ r\), \(0\leq r\leq k-1\). Then, if \(G\) has minimum degree at least \((s- 1)k\), it contains \(k\) independent cycles \(C_ 1, C_ 2,\dots, C_ k\) such that the length of \(C_ i\) is inclusively between \(s\) and \(q\) for \(1\leq i\leq k- r\) and inclusively between \(s\) and \(q+ 1\) for \(k- r< i\leq k\).
scientific article; zbMATH DE number 700944