The maximum degree of a minimally Hamiltonian-connected graph. (English) Zbl 1497.05041
Summary: We determine the possible maximum degrees of a minimally Hamiltonian-connected graph with a given order. This answers a question posed by M. Modalleliyan and B. Omoomi [Ars Comb. 126, 13–27 (2016; Zbl 1413.05205)]. We also pose two unsolved problems.
Citations:
Zbl 1413.05205References:
| [1] | Bian, Q.; Gould, R. J.; Horn, P.; Janiszewski, S.; Fleur, S. L.; Wrayno, P., 3-connected \(\{ K_{1 , 3}, P_9 \}\)-free graphs are hamiltonian-connected, Graphs Comb., 30, 1099-1122 (2014) · Zbl 1298.05189 |
| [2] | Modalleliyan, M.; Omoomi, B., Critical hamiltonian-connected graphs, Ars Comb., 126, 13-27 (2016) · Zbl 1413.05205 |
| [3] | Ryjáček, Z.; Vrána, P., Every 3-connected \(\{ K_{1 , 3}, Z_7 \}\)-free graph of order at least 21 is Hamilton-connected, Discrete Math., 344, Article 112350 pp. (2021) · Zbl 1469.05100 |
| [4] | Vrána, P.; Zhan, X.; Zhang, L., Proof of a conjecture on hamiltonian-connected graphs, Discrete Math., 345, 8, Article 112909 pp. (2022) · Zbl 1490.05150 |
| [5] | West, D. B., Introduction to Graph Theory (1996), Prentice Hall, Inc. · Zbl 0845.05001 |
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