On the dimension of Archimedean solids

• Autorzy: Madaras T. , Siroczki P.
• Języki publikacji: EN

Abstrakty

EN

We study the dimension of graphs of the Archimedean solids. For most of these graphs we find the exact value of their dimension by finding unit-distance embeddings in the euclidean plane or by proving that such an embedding is not possible.

Słowa kluczowe

EN

Archimedean solid; unit-distance graph; dimension of a graph

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2014
• Tom: Vol. 34, no. 1
• Strony: 123--138
• Opis fizyczny: Bibliogr. 7 poz., rys., tab.

Twórcy

autor

Madaras T.

• Institute of Mathematics, Faculty of Sciences University of P. J. Šafárik Jesenná 5, 041 54 Košice, Slovak Republic

autor

Siroczki P.

• Institute of Mathematics, Faculty of Sciences University of P. J. Šafárik Jesenná 5, 041 54 Košice, Slovak Republic

Bibliografia

• [1] R. Diestel, Graph Theory, Springer, 2006.
• [2] D. Eppstein, Unit distance graphs, 2010, Blog posting at http://11011110.livejournal.com/188807.html.
• [3] P. Erdos, F. Harary, W.T. Tutte, On the dimension of a graph, Mathematika 12 (1965), 118–122.
• [4] E.H.-A. Gerbracht, Eleven unit distance embeddings of the Heawood graph, arXiv:0912.5395.
• [5] B. Grünbaum, An enduring error, Elemente der Mathematik 64 (2009), 89–101.
• [6] R. Hochberg, A program for proving that a given graph is not a unit-distance graph: preliminary report, [in:] Proceedings of the 44th Annual Southeast Regional Conference, Melbourne, Florida, March 10–12, 2006, 768–769.
• [7] B. Horvat, T. Pisanski, A. Žitnik, All generalized Petersen graphs are unit-distance graphs, J. Korean Math. Soc. 49 (2012), 475–491.