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

Oleg V. Borodin; Douglas R. Woodall

Discussiones Mathematicae Graph Theory (1998)

- Volume: 18, Issue: 2, page 159-164
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topOleg V. Borodin, and Douglas R. Woodall. "Short cycles of low weight in normal plane maps with minimum degree 5." Discussiones Mathematicae Graph Theory 18.2 (1998): 159-164. <http://eudml.org/doc/270522>.

@article{OlegV1998,

abstract = {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.},

author = {Oleg V. Borodin, Douglas R. Woodall},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {planar graphs; plane triangulation; light subgraphs; weight},

language = {eng},

number = {2},

pages = {159-164},

title = {Short cycles of low weight in normal plane maps with minimum degree 5},

url = {http://eudml.org/doc/270522},

volume = {18},

year = {1998},

}

TY - JOUR

AU - Oleg V. Borodin

AU - Douglas R. Woodall

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

JO - Discussiones Mathematicae Graph Theory

PY - 1998

VL - 18

IS - 2

SP - 159

EP - 164

AB - 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.

LA - eng

KW - planar graphs; plane triangulation; light subgraphs; weight

UR - http://eudml.org/doc/270522

ER -

## References

top- [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. Zbl0877.05050
- [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.

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.