Neighborhood Unions for the Existence of Disjoint Chorded Cycles in Graphs |
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| Authors: | Yunshu Gao Guojun Li Jin Yan |
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| Institution: | 1. School of Mathematics and Computer Science, Ningxia University, Ningxia, 750021, People’s Republic of China
2. School of Mathematics, Shandong University, Jinan, 250100, People’s Republic of China
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| Abstract: | A chorded cycle is a cycle with at least one chord. We prove that if G is a simple graph with order n ≥ 4k and ${|N_G(x)\cup N_G(y)|\geq 4k+1}$ for each nonadjacent pair of vertices x and y, then G contains k vertex-disjoint chorded cycles. The degree condition is sharp in general. |
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