Hamiltonian connectedness and a matching in powers of connected graphs

Elena Wisztová

Mathematica Bohemica (1995)

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

Abstract

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In this paper the following results are proved: 1. Let P n be a path with n vertices, where n ≥ 5 and n ≠ 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 ≥ 5 , and let M be a matching in G . Then G 5 - M is hamiltonian-connected.

How to cite

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Wisztová, 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

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  1. M. Behzad G. Chartrand L. Lesniak-Foster, Graphs & Digraphs, Prindle, Weber & Schmidt, Boston 1979. (1979) MR0525578
  2. F. Harary, Graph Theory, Addison-Wesley, Reading (Mass.), 1969. (1969) Zbl0196.27202MR0256911
  3. L. Nebeský, A matching and a hamiltonian cycle of the fourth power of a connected graph, Mathematica Bohemica 118 (1993), 43-52. (1993) MR1213832
  4. J. Sedláček, Introduction Into the Graph Theory, Academia, Praha, 1981. (In Czech.) (1981) 
  5. 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
  6. 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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