Abstract
In this paper, we characterize connected \(\{K_{1,3},N(2,1,0)\}\)-free but not \(N(1,1,1)\)-free graphs. By combining our result and a theorem showed by Duffus et al. (every \(2\)-connected \(\{K_{1,3},N(1,1,1)\}\)-free graph is Hamiltonian), we give an alternative proof of Bedrossian’s theorem (every \(2\)-connected \(\{K_{1,3},N(2,1,0)\}\)-free graph is Hamiltonian).
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Furuya, M., Tsuchiya, S. Claw-Free and \(N(2,1,0)\)-Free Graphs are Almost Net-Free. Graphs and Combinatorics 31, 2201–2205 (2015). https://doi.org/10.1007/s00373-014-1506-1
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DOI: https://doi.org/10.1007/s00373-014-1506-1