Geodesic
A matching and a Hamiltonian cycle of the fourth power of a connected graph
Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 43-52

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

MR Zbl
The following result is proved: Let $G$ be a connected graph of order $geq 4$. Then for every matching $M$ in $G^4$ there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.
The following result is proved: Let $G$ be a connected graph of order $geq 4$. Then for every matching $M$ in $G^4$ there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.
DOI : 10.21136/MB.1993.126012
Classification : 05C38, 05C40, 05C45, 05C70
Keywords: matching; factors; Hamiltonian cycles; powers of graphs; connected graph 
Nebeský, Ladislav. A matching and a Hamiltonian cycle of the fourth power of a connected graph. Mathematica Bohemica, Tome 118 (1993) no. 1, pp. 43-52. doi: 10.21136/MB.1993.126012
@article{10_21136_MB_1993_126012,
     author = {Nebesk\'y, Ladislav},
     title = {A matching and a {Hamiltonian} cycle of the fourth power of a connected graph},
     journal = {Mathematica Bohemica},
     pages = {43--52},
     year = {1993},
     volume = {118},
     number = {1},
     doi = {10.21136/MB.1993.126012},
     mrnumber = {1213832},
     zbl = {0780.05046},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126012/}
}
TY  - JOUR
AU  - Nebeský, Ladislav
TI  - A matching and a Hamiltonian cycle of the fourth power of a connected graph
JO  - Mathematica Bohemica
PY  - 1993
SP  - 43
EP  - 52
VL  - 118
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126012/
DO  - 10.21136/MB.1993.126012
LA  - en
ID  - 10_21136_MB_1993_126012
ER  - 
%0 Journal Article
%A Nebeský, Ladislav
%T A matching and a Hamiltonian cycle of the fourth power of a connected graph
%J Mathematica Bohemica
%D 1993
%P 43-52
%V 118
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.1993.126012/
%R 10.21136/MB.1993.126012
%G en
%F 10_21136_MB_1993_126012

[1] M. Behzad G. Chartrand, and L. Lesniak-Foster: Graphs & Digraphs. Prindle, Weber L Schmidt, Boston, 1979. | MR

[2] G. Chartrand A. D. PoUmeni, and M. J. Stewart: The existence of 1-factors in line graphs, squares and total graphs. Indag. Math. 35 (1973), 228-232. | DOI | MR

[3] L. Nebeský: On the existence of a 3-factor in the fourth power of graph. Časopis pěst. mat. 105 (1980), 204-207. | MR

[4] L. Nebeský: On a 1-factor of the fourth power of a connected graph. Časopis pěst. mat. 113 (1988), 415-420. | MR

[5] M. Sekanina: On an ordering of the set of vertices of a connected graph. Publ. Sci. Univ. Brno 412 (1960), 137-142. | MR | Zbl

[6] D. P. Sumner: Graphs with 1-factors. Proc. Amer. Math. Soc. 42 (1974), 8-12. | MR | Zbl

[7] E. Wisztová: A hamiltonian cycle and a 1-factor on the fourth power of a graph. Časopis pěst. mat. 110 (1985), 403-412. | MR

[8] E. Wisztová: On a hamiltonian cycle of the fourth power of a connected graph. Mathematica Bohemica 116 (1991), 385-390. | MR

Cité par Sources :