On long cycles through four prescribed vertices of a polyhedral graph

• Autorzy: Jochen Harant , Stanislav Jendrol' , Hansjoachim Walther
• Języki publikacji: EN

Abstrakty

EN

For a 3-connected planar graph G with circumference c ≥ 44 it is proved that G has a cycle of length at least (1/36)c+(20/3) through any four vertices of G.

Słowa kluczowe

EN

graph; long cycle; prescribed vertices

Kategorie tematyczne

• 05C38: Paths and cycles

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2008
• Tom: 28
• Numer: 3
• Strony: 441-451

Daty

wydano

2008

otrzymano

2007-07-31

poprawiono

2008-06-03

zaakceptowano

2008-06-03

Twórcy

autor

Jochen Harant

• Institute of Mathematics, Technical University Ilmenau, Germany

autor

Stanislav Jendrol'

• Institute of Mathematics, P.J. Šafárik University Košice, Slovakia

autor

Hansjoachim Walther

• Institute of Mathematics, Technical University Ilmenau, Germany

Bibliografia

• [1] T. Böhme, F. Göring and J. Harant, Menger's theorem, J. Graph Theory 37 (2001) 35-36, doi: 10.1002/jgt.1001.
• [2] R. Diestel, Graph Theory (Springer, Graduate Texts in Mathematics 173, 2000).
• [3] 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.
• [4] L. Lovász, Combinatorial problems and exercises (Akadémiai Kiadó, Budapest, Hungary 1979) Section 6, Problem 42.
• [5] J.W. Moon and L. Moser, Simple paths on polyhedra, Pacific J. Math. 13 (1963) 629-631.
• [6] A. Saito, Long cycles through specified vertices in a graph, J. Combin. Theory (B) 47 (1989) 220-230, doi: 10.1016/0095-8956(89)90021-X.
• [7] W.T. Tutte, A theorem on planar graphs, Trans. Amer. Math. Soc. 82 (1956) 99-116, doi: 10.1090/S0002-9947-1956-0081471-8.
• [8] W.T. Tutte, Bridges and Hamiltonian circuits in planar graphs, Aequationes Math. 15 (1977) 1-33, doi: 10.1007/BF01837870.

Identyfikatory

DOI

10.7151/dmgt.1418