Minimal unavoidable sets of cycles in plane graphs

• Autorzy: Madaras T. , Tamasova M.

Identyfikatory

DOI

10.7494/OpMath.2018.38.6.859

• Języki publikacji: EN

Abstrakty

EN

A set S of cycles is minimal unavoidable in a graph family [formula] if each graph [formula] contains a cycle from S and, for each proper subset S' ⊂ S, there exists an infinite subfamily [formula] such that no graph from [formula] contains a cycle from S'. In this paper, we study minimal unavoidable sets of cycles in plane graphs of minimum degree at least 3 and present several graph constructions which forbid many cycle sets to be unavoidable. We also show the minimality of several small sets consisting of short cycles

Słowa kluczowe

EN

plane graph; polyhedral graph; set of cycles

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2018
• Tom: Vol. 38, no. 6
• Strony: 859--870
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Madaras T.

• Pavol Józef Śafarik University Faculty of Science Institute of Mathematics Jesenna 5, 04001 Kosice, Slovakia

autor

Tamasova M.

• Pavol Józef Śafarik University Faculty of Science Institute of Mathematics Jesenna 5, 04001 Kosice, Slovakia

Bibliografia

• [1] J. Bensmail, On q-power cycles in cubic graphs, Discuss. Math. Graph Theory 37 (2017), 211-220.
• [2] O.V. Borodin, Solution of problems of Kotzig and Grunbaum concerning the isolation of cycles in planar graphs, Math. Notes 46 (1989), 835-837 (English translation), Mat. Zametki 46 (1989), 9-12 [in Russian].
• [3] G. Exoo, Three graphs and the Erdos-Gydrfds conjecture, arXiv: 1403.5636 [math.CO].
• [4] C.C. Heckman, R. Krakovski, Erdos-Gydrfds conjecture for cubic planar graphs, Electron. J. Combin. 20 (2013) P7.
• [5] S. JendroF, P.J. Owens, On light graphs in 3-connected plane graphs without triangular or quadrangular faces, Graphs and Combinatorics 17 (2001) 4, 659-680.
• [6] A. Kotzig, Contribution to the theory of Eulerian polyhedra, Mat. Cas. SAV (Math. Slovaca) 5 (1955), 101-113.
• [7] T. Madaras, M. Tamasova, Minimal unavoidable sets of cycles in polyhedral graphs, manuscript.
• [8] P. Wernicke, Uber den kartographischen Vierfarbensatz, Math. Ann. 58 (1904), 413-426. [9] D. West, Introduction to Graph Theory, 2nd ed., Prentice Hall, 2001.

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).