3-Connected {K1,3, P9}-Free Graphs are Hamiltonian-Connected |
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| Authors: | Qiuju Bian Ronald J. Gould Paul Horn Susan Janiszewski Steven La Fleur Paul Wrayno |
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| Affiliation: | 1.School of Mathematics and Information Science,Shandong University of Technology,Zibo,People’s Republic of China;2.Department of Mathematics and Computer Science,Emory University,Atlanta,USA;3.Department of Mathematics, FAS,Harvard University,Cambridge,USA;4.Department of Mathematics,Western Kentucky University,Bowling Green,USA |
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| Abstract: | We investigate pairs of forbidden subgraphs that imply a 3-connected graph is Hamiltonian-connected. In particular we show that the pair {K 1,3, P 9} is such a pair. As it is known that P 10 cannot replace P 9, this result is best possible. Further, we show that certain other graphs are not possible. |
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