To solve the existence problem of 2-factors in claw-free graphs,a sufficient condition for 2-factors in 2-connected claw-free graphs under the condition of independence number is proposed.Since the existence problem of 2-factors,like the Hamiltonian problem,is an NP-complete problem,the 2-factor strengthened closure proposed by Ryjáček is used as a tool to transform the 2-factor in claw-free graphs into d-system of the original graph of a certain line graph.By using the reductio ad absurdum meth-od,through the characteristics of the girth and circumference of the original graph of the line graph after the closure transformation,the topological structure is discussed and analyzed in different cases,thereby completely characterizing the 2-factor of 2-connected claw-free graphs under the condition of independence number.This further reveals the topological structure of claw-free graphs under the condition of independ-ence number and provides new ideas and methods for the future research of 2-factors.
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