Abstract
For non-negative integers i, j and k, let N i,j,k be the graph obtained by identifying end vertices of three disjoint paths of lengths i, j and k to the vertices of a triangle. In this paper, we prove that every 3-connected {K 1,3,N 3,3,3}-free graph is Hamiltonian. This result is sharp in the sense that for any integer i > 3, there exist infinitely many 3-connected {K 1,3,N i,3,3}-free non-Hamiltonian graphs.
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Lin, H., Hu, Z. Every 3-connected {K 1,3,N 3,3,3}-free graph is Hamiltonian. Sci. China Math. 56, 1585–1595 (2013). https://doi.org/10.1007/s11425-013-4631-z
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DOI: https://doi.org/10.1007/s11425-013-4631-z