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Every 3-connected {K 1,3,N 3,3,3}-free graph is Hamiltonian |
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| Authors: | HouYuan Lin ZhiQuan Hu |
| Affiliation: | 14631. School of Mathematics and Quantitative Economics, Shandong University of Finance and Economics, Jinan, 250014, China 24631. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China |
| 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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