| Title:
|
On a Hamiltonian cycle of the fourth power of a connected graph (English) |
| Author:
|
Wisztová, Elena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
116 |
| Issue:
|
4 |
| Year:
|
1991 |
| Pages:
|
385-390 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\geq 4$ and let $M$ be a matching in $G$. Then there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$. (English) |
| Keyword:
|
Hamiltonian cycle |
| Keyword:
|
power of connected graph |
| Keyword:
|
matching |
| Keyword:
|
powers of graphs |
| Keyword:
|
matching in graphs |
| MSC:
|
05C38 |
| MSC:
|
05C45 |
| MSC:
|
05C75 |
| idZBL:
|
Zbl 0752.05039 |
| idMR:
|
MR1146396 |
| DOI:
|
10.21136/MB.1991.126033 |
| . |
| Date available:
|
2009-09-24T20:47:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126033 |
| . |
| Reference:
|
[1] M. Behzad G. Chartrand L. Lesniak-Foster: Graphs & Digraphs.Prindle. Weber & Schmidt, Boston 1979. MR 0525578 |
| Reference:
|
[2] F. Harary: Graph Theory.Addison-Wesley, Reading, Mass., 1969. Zbl 0196.27202, MR 0256911 |
| Reference:
|
[3] L. Nebeský: On the existence of a 3-factor in the fourth power of a graph.Čas. pěst. mat. 105 (1980), 204-207. MR 0573113 |
| Reference:
|
[4] L. Nebeský: Edge-disjoint 1-factors in powers of connected graphs.Czech. Math. J. 34 (109) (1984), 499-505. MR 0764434 |
| Reference:
|
[5] L. Nebeský: On a 1-factor of the fourth power of a connected graph.Čas. pěst. mat. 113 (1988), 415-420. MR 0981882 |
| Reference:
|
[6] J. Sedláček: Introduction into the Graph Theory.(Czech). Academia nakl. ČSAV, Praha 1981. |
| Reference:
|
[7] E. Wisztová: A hamiltonian cycle and a 1-factor in the fourth power of a graph.Čas. pěst. mat. 110 (1985), 403-412. MR 0820332 |
| . |
