2025/04/13 by Lu, Zaiping, Xue, Shudan
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.09477
A chorded cycle in a graph G is a cycle on which two nonadjacent vertices are adjacent in the graph G. In 2010, Gao and Qiao independently proved a graph of order at least 4s, in which the neighborhood union of any two nonadjacent vertices has at least 4s+1 vertices, contains s vertex-disjoint chorded cycles. In 2022, Gould raised a problem that asks whether increasing connectivity would improve the neighborhood union condition. In this paper, we solve the problem for 2-connected graphs by proving that a 2-connected graph of order at least 4s, in which the neighborhood union of any two nonadjacent vertices has at least 4s vertices, contains s vertex-disjoint chorded cycles.