Short cycles of low weight in normal plane maps with minimum degree 5

• Autorzy: Oleg V. Borodin , Douglas R. Woodall
• Języki publikacji: EN

Abstrakty

EN

In this note, precise upper bounds are determined for the minimum degree-sum of the vertices of a 4-cycle and a 5-cycle in a plane triangulation with minimum degree 5: w(C₄) ≤ 25 and w(C₅) ≤ 30. These hold because a normal plane map with minimum degree 5 must contain a 4-star with $w(K_{1,4}) ≤ 30$. These results answer a question posed by Kotzig in 1979 and recent questions of Jendrol' and Madaras.

Słowa kluczowe

EN

planar graphs; plane triangulation

Kategorie tematyczne

• 05C10: Planar graphs; geometric and topological aspects of graph theory
• 05C38: Paths and cycles
• 05C75: Structural characterization of families of graphs

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 1998
• Tom: 18
• Numer: 2
• Strony: 159-164

Daty

wydano

1998

otrzymano

1997-08-29

poprawiono

1998-03-25

Twórcy

autor

Oleg V. Borodin

• Novosibirsk State University, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090, Russia

autor

Douglas R. Woodall

• Department of Mathematics, University of Nottingham, Nottingham, NG7 2RD, England

Bibliografia

• [1] O.V. Borodin, Solution of Kotzig's and Grünbaum's problems on the separability of a cycle in a planar graph, Matem. Zametki 46 (5) (1989) 9-12. (in Russian)
• [2] O.V. Borodin and D.R. Woodall, Vertices of degree 5 in plane triangulations (manuscript, 1994).
• [3] S. Jendrol' and T. Madaras, On light subgraphs in plane graphs of minimal degree five, Discussiones Math. Graph Theory 16 (1996) 207-217, doi: 10.7151/dmgt.1035.
• [4] A. Kotzig, From the theory of eulerian polyhedra, Mat. Cas. 13 (1963) 20-34. (in Russian)
• [5] A. Kotzig, Extremal polyhedral graphs, Ann. New York Acad. Sci. 319 (1979) 569-570.

Identyfikatory

DOI

10.7151/dmgt.1071