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Vertex-disjoint chorded cycles in a graph. (English) Zbl 1227.05175

Summary: We prove: Let \(k\geq 1\) be an integer and \(G\) be graph with at least \(4k\) vertices and minimum degree at least \(\lfloor 7k/2\rfloor \). Then \(G\) contains \(k\) vertex-disjoint cycles such that each of them has at least two chords in \(G\).

MSC:

05C38 Paths and cycles
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References:

[1] Bondy, J. A.; Murty, U. S.R., Graph Theory with Applications (1976), Macmillan Press: Macmillan Press New York · Zbl 1134.05001
[2] Corrádi, K.; Hajnal, A., On the maximal number of independent circuits in a graph, Acta Math. Acad. Sci. Hungr., 14, 423-439 (1963) · Zbl 0118.19001
[3] Czipser, Solution to problem 127 (Hungarian), Mat. Lapok, 14, 373-374 (1963)
[4] Finkel, D., On the number of independent chorded cycles in a graph, Discrete Math., 308, 5265-5268 (2008) · Zbl 1228.05170
[5] Pósa, L., Problem no. 127 (Hungarian), Mat. Lapok, 12, 254 (1961)
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