On short cycles through prescribed vertices of a polyhedral graph

• Autorzy: Erhard Hexel
• Języki publikacji: EN

Abstrakty

EN

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

Słowa kluczowe

EN

polyhedral graph; triangulation; short cycle; prescribed vertices

Kategorie tematyczne

• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2005
• Tom: 25
• Numer: 3
• Strony: 419-426

Daty

wydano

2005

otrzymano

2004-09-03

poprawiono

2005-02-18

Twórcy

autor

Erhard Hexel

• Department of Mathematics, Technische Universität Ilmenau, Postfach 0565, D-98684 Ilmenau, Germany

Bibliografia

• [1] B. Bollobás and G. Brightwell, Cycles through specified vertices, Combinatorica 13 (1993) 147-155, doi: 10.1007/BF01303200.
• [2] G.A. Dirac, 4-crome Graphen und vollständige 4-Graphen, Math. Nachr. 22 (1960) 51-60, doi: 10.1002/mana.19600220106.
• [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.
• [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.
• [7] T. Sakai, Long paths and cycles through specified vertices in k-connected graphs, Ars Combin. 58 (2001) 33-65.

Identyfikatory

DOI

10.7151/dmgt.1293