Abstract
For integers i, j, k with \({i\geq j\geq k\geq 0}\), let N i, j, k be the graph obtained by identifying end vertices of three disjoint paths of lengths i, j, k to the vertices of a triangle. In this paper, we show that every 3-connected {K 1,3, N i, 7-i, 2}-free graph is hamiltonian, where \({i \in \{4,5\}}\) . This result is sharp in the sense that no one of the numbers i, 7−i and 2 in N i, 7-i, 2 can be replaced by a larger number.
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Financially supported by NSFC grants 11071096 and 11271149, the Special Fund CCNU11A02015 for Basic Scientific Research of Central Colleges, grant D20111110 of Hubei Provincial Department of Education, and grant 20110205 of Jinan Science and Technology Bureau.
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Hu, Z., Lin, H. Two Forbidden Subgraph Pairs for Hamiltonicity of 3-Connected Graphs. Graphs and Combinatorics 29, 1755–1775 (2013). https://doi.org/10.1007/s00373-012-1245-0
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DOI: https://doi.org/10.1007/s00373-012-1245-0