| Title:
|
Hamiltonian connectedness and a matching in powers of connected graphs (English) |
| Author:
|
Wisztová, Elena |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
120 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
305-317 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, where $n \geq5$ and $n \not= 7,8$. Let $M$ be a matching in $P_n$. Then $(P_n)^4 - M$ is hamiltonian-connected. 2. Let $G$ be a connected graph of order $p \geq5$, and let $M$ be a matching in $G$. Then $G^5 - M$ is hamiltonian-connected. (English) |
| Keyword:
|
power |
| Keyword:
|
distance |
| Keyword:
|
matching |
| Keyword:
|
hamiltonian path |
| Keyword:
|
hamiltonian connected |
| Keyword:
|
power of a graph |
| MSC:
|
05C12 |
| MSC:
|
05C45 |
| MSC:
|
05C70 |
| idZBL:
|
Zbl 0848.05047 |
| idMR:
|
MR1369689 |
| DOI:
|
10.21136/MB.1995.126003 |
| . |
| Date available:
|
2009-09-24T21:12:14Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126003 |
| . |
| 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: A matching and a hamiltonian cycle of the fourth power of a connected graph.Mathematica Bohemica 118 (1993), 43-52. MR 1213832 |
| Reference:
|
[4] J. Sedláček: Introduction Into the Graph Theory.Academia, Praha, 1981. (In Czech.) |
| Reference:
|
[5] M. Sekanina: On an ordering of the set of vertices of a connected graph.Publ. Sci. Univ. Brno 412 (1960), 137-142. Zbl 0118.18903, MR 0140095 |
| Reference:
|
[6] E. Wisztová: On a hamiltonian cycle of the fourth power of a connected graph.Mathematica Bohemica 116 (1991), 385-390. MR 1146396 |
| . |
