# On short cycles through prescribed vertices of a polyhedral graph

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 419-426
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topErhard Hexel. "On short cycles through prescribed vertices of a polyhedral graph." Discussiones Mathematicae Graph Theory 25.3 (2005): 419-426. <http://eudml.org/doc/270742>.

@article{ErhardHexel2005,

abstract = {Guaranteed upper bounds on the length of a shortest cycle through k ≤ 5 prescribed vertices of a polyhedral graph or plane triangulation are proved.},

author = {Erhard Hexel},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {polyhedral graph; triangulation; short cycle; prescribed vertices},

language = {eng},

number = {3},

pages = {419-426},

title = {On short cycles through prescribed vertices of a polyhedral graph},

url = {http://eudml.org/doc/270742},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Erhard Hexel

TI - On short cycles through prescribed vertices of a polyhedral graph

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 419

EP - 426

AB - Guaranteed upper bounds on the length of a shortest cycle through k ≤ 5 prescribed vertices of a polyhedral graph or plane triangulation are proved.

LA - eng

KW - polyhedral graph; triangulation; short cycle; prescribed vertices

UR - http://eudml.org/doc/270742

ER -

## References

top- [1] B. Bollobás and G. Brightwell, Cycles through specified vertices, Combinatorica 13 (1993) 147-155, doi: 10.1007/BF01303200. Zbl0780.05033
- [2] G.A. Dirac, 4-crome Graphen und vollständige 4-Graphen, Math. Nachr. 22 (1960) 51-60, doi: 10.1002/mana.19600220106. Zbl0096.17902
- [3] F. Göring, J. Harant, E. Hexel and Zs. Tuza, On short cycles through prescribed vertices of a graph, Discrete Math. 286 (2004) 67-74, doi: 10.1016/j.disc.2003.11.047.
- [4] J. Harant, On paths and cycles through specified vertices, Discrete Math. 286 (2004) 95-98, doi: 10.1016/j.disc.2003.11.059. Zbl1048.05050
- [5] R. Diestel, Graph Theory (Springer, Graduate Texts in Mathematics 173, 2000).
- [6] A.K. Kelmans and M.V. Lomonosov, When m vertices in a k-connected graph cannot be walked round along a simple cycle, Discrete Math. 38 (1982) 317-322, doi: 10.1016/0012-365X(82)90299-0. Zbl0475.05053
- [7] T. Sakai, Long paths and cycles through specified vertices in k-connected graphs, Ars Combin. 58 (2001) 33-65. Zbl1065.05059

## NotesEmbed ?

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