Claw-Free and $N(2,1,0)$-Free Graphs are Almost Net-Free

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).