# Hamiltonian connectedness and a matching in powers of connected graphs

Mathematica Bohemica (1995)

- Volume: 120, Issue: 3, page 305-317
- ISSN: 0862-7959

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topWisztová, Elena. "Hamiltonian connectedness and a matching in powers of connected graphs." Mathematica Bohemica 120.3 (1995): 305-317. <http://eudml.org/doc/247814>.

@article{Wisztová1995,

abstract = {In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, where $n \ge 5$ and $n \ne 7,8$. 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 $p \ge 5$, and let $M$ be a matching in $G$. Then $G^5 - M$ is hamiltonian-connected.},

author = {Wisztová, Elena},

journal = {Mathematica Bohemica},

keywords = {power; distance; matching; hamiltonian path; hamiltonian connected; power of a graph; power; distance; matching; hamiltonian path; hamiltonian connected},

language = {eng},

number = {3},

pages = {305-317},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Hamiltonian connectedness and a matching in powers of connected graphs},

url = {http://eudml.org/doc/247814},

volume = {120},

year = {1995},

}

TY - JOUR

AU - Wisztová, Elena

TI - Hamiltonian connectedness and a matching in powers of connected graphs

JO - Mathematica Bohemica

PY - 1995

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 120

IS - 3

SP - 305

EP - 317

AB - In this paper the following results are proved: 1. Let $P_n$ be a path with $n$ vertices, where $n \ge 5$ and $n \ne 7,8$. 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 $p \ge 5$, and let $M$ be a matching in $G$. Then $G^5 - M$ is hamiltonian-connected.

LA - eng

KW - power; distance; matching; hamiltonian path; hamiltonian connected; power of a graph; power; distance; matching; hamiltonian path; hamiltonian connected

UR - http://eudml.org/doc/247814

ER -

## References

top- M. Behzad G. Chartrand L. Lesniak-Foster, Graphs & Digraphs, Prindle, Weber & Schmidt, Boston 1979. (1979) MR0525578
- F. Harary, Graph Theory, Addison-Wesley, Reading (Mass.), 1969. (1969) Zbl0196.27202MR0256911
- L. Nebeský, A matching and a hamiltonian cycle of the fourth power of a connected graph, Mathematica Bohemica 118 (1993), 43-52. (1993) MR1213832
- J. Sedláček, Introduction Into the Graph Theory, Academia, Praha, 1981. (In Czech.) (1981)
- M. Sekanina, On an ordering of the set of vertices of a connected graph, Publ. Sci. Univ. Brno 412 (1960), 137-142. (1960) Zbl0118.18903MR0140095
- E. Wisztová, On a hamiltonian cycle of the fourth power of a connected graph, Mathematica Bohemica 116 (1991), 385-390. (1991) MR1146396

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