Universal planar graphs for the topological minor relation. (English) Zbl 07829399
References:
| [1] | Diestel, R., On universal graphs with forbidden topological subgraphs, Eur. J. Comb., 6, 175-182, 1985 · Zbl 0581.05020 · doi:10.1016/S0195-6698(85)80008-1 |
| [2] | Diestel, R., Graph Theory. Graduate Texts in Mathematics, 2017, Berlin: Springer, Berlin · Zbl 1375.05002 |
| [3] | Diestel, R.; Halin, R.; Vogler, W., Some remarks on universal graphs, Combinatorica, 5, 283-293, 1985 · Zbl 0619.05039 · doi:10.1007/BF02579242 |
| [4] | Diestel, R.; Kühn, D., A universal planar graph under the minor relation, J. Graph Theory, 32, 2, 191-206, 1999 · Zbl 0932.05025 · doi:10.1002/(SICI)1097-0118(199910)32:2<191::AID-JGT8>3.0.CO;2-I |
| [5] | Dirac, GA; Schuster, S., A theorem of Kuratowski, Nederl. Akad. Wet. Proc. Ser. A, 57, 343-348, 1954 · Zbl 0055.17002 |
| [6] | Georgakopoulos, A.: On graph classes with minor-universal elements (2022). Preprint, arXiv:2212.05498 |
| [7] | Henson, CW, A family of countable homogeneous graphs, Pac. J. Math., 38, 69-83, 1971 · Zbl 0219.05064 · doi:10.2140/pjm.1971.38.69 |
| [8] | Huynh, T., Mohar, B., Šámal, R., Thomassen, C., Wood, D.R.: Universality in minor-closed graph classes (2021). Preprint, arXiv:2109.00327 |
| [9] | Komjáth, P.; Pach, J., Universal elements and the complexity of certain classes of infinite graphs, Discret. Math., 95, 1-3, 255-270, 1991 · Zbl 0756.05097 · doi:10.1016/0012-365X(91)90340-8 |
| [10] | Krill, T.: On universal graphs with forbidden substructures. Master’s thesis, Universität Hamburg (2021) |
| [11] | Krill, T.: Universal graphs for the topological minor relation. J. Graph Theory (2023) to appear · Zbl 1526.05106 |
| [12] | Kühn, D., Minor-universal planar graphs without accumulation points, J. Graph Theory, 36, 1, 1-7, 2001 · Zbl 0971.05104 · doi:10.1002/1097-0118(200101)36:1<1::AID-JGT1>3.0.CO;2-B |
| [13] | Lehner, F., A note on classes of subgraphs of locally finite graphs, J. Comb. Theory Ser. B, 161, 52-62, 2023 · Zbl 1512.05300 · doi:10.1016/j.jctb.2023.02.001 |
| [14] | Pach, J., A problem of Ulam on planar graphs, Eur. J. Comb., 2, 357-361, 1981 · Zbl 0469.05027 · doi:10.1016/S0195-6698(81)80043-1 |
| [15] | Rado, R., Universal graphs and universal functions, Acta Arith., 9, 331-340, 1964 · Zbl 0139.17303 · doi:10.4064/aa-9-4-331-340 |
| [16] | Wagner, K., Fastplättbare Graphen, J. Comb. Theory, 3, 326-365, 1967 · Zbl 0153.54101 · doi:10.1016/S0021-9800(67)80103-0 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
