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On independent triples and vertex-disjoint chorded cycles in graphs. (English) Zbl 1444.05077
Summary: Let $$G$$ be a graph, and let $$\sigma_3(G)$$ be the minimum degree sum of three independent vertices of $$G$$. We prove that if $$G$$ is a graph of order at least $$8k+5$$ and $$\sigma_3(G)\geq 9k-2$$ with $$k\geq 1$$, then $$G$$ contains $$k$$ vertex-disjoint chorded cycles. We also show that the degree sum condition on $$\sigma_3(G)$$ is sharp.
##### MSC:
 05C38 Paths and cycles
##### Keywords:
degree sum condition; chorded cycle
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##### References:
 [1] S. Chiba, S. Fujita, Y. Gao and G. Li, On a sharp degree sum condition for disjoint chorded cycles in graphs,Graphs Combin.26 (2010), 173-186. · Zbl 1231.05143 [2] S. Chiba and T. Yamashita, Degree conditions for the existence of vertex-disjoint cycles and paths: A survey,Graphs Combin.34 (2018), 1-83. · Zbl 1382.05017 [3] K. Corr´adi and A. Hajnal, On the maximal number of independent circuits in a graph,Acta Math. Acad. Sci. Hungar.14 (1963), 423-439. [4] H. Enomoto, On the existence of disjoint cycles in a graph,Combinatorica18 (4) (1998), 487-492. · Zbl 0924.05041 [5] D. Finkel, On the number of independent chorded cycles in a graph,Discrete Math.308 (22) (2008), 5265-5268. · Zbl 1228.05170 [6] S. Fujita, H. Matsumura, M. Tsugaki and T. Yamashita, Degree sum conditions and vertex-disjoint cycles in a graph,Australas. J. Combin.35 (2006), 237-251. · Zbl 1096.05029 [7] Y. Gao, X. Lin and H. Wang, Vertex-disjoint double chorded cycles in bipartite graphs,Discrete Math.342 (9) (2019), 2482-2492. · Zbl 1416.05226 [8] R. J. Gould, Graph Theory, Dover Pub. Inc. Mineola, N.Y. 2012. · Zbl 1284.05003 [9] R. J. Gould, K. Hirohata and A. Keller, On vertex-disjoint cycles and degree sum conditions,Discrete Math.341 (1) (2018), 203-212. · Zbl 1372.05111 [10] T. Molla, M. Santana and E. Yeager, Disjoint cycles and chorded cycles in a graph with given minimum degree,Discrete Math.343 (6) (2020), 111837. · Zbl 1437.05117 [11] H.
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