On a Hamiltonian cycle of the fourth power of a connected graph

Elena Wisztová

Mathematica Bohemica (1991)

  • Volume: 116, Issue: 4, page 385-390
  • ISSN: 0862-7959

Abstract

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In this paper the following theorem is proved: Let G be a connected graph of order p ≥ 4 and let M be a matching in G . Then there exists a hamiltonian cycle C of G 4 such that E ( C ) ⋂ M = 0 .

How to cite

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Wisztová, Elena. "On a Hamiltonian cycle of the fourth power of a connected graph." Mathematica Bohemica 116.4 (1991): 385-390. <http://eudml.org/doc/29187>.

@article{Wisztová1991,
abstract = {In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\ge 4$ and let $M$ be a matching in $G$. Then there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.},
author = {Wisztová, Elena},
journal = {Mathematica Bohemica},
keywords = {Hamiltonian cycle; power of connected graph; matching; powers of graphs; matching in graphs; Hamiltonian cycle; power of connected graph; matching},
language = {eng},
number = {4},
pages = {385-390},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On a Hamiltonian cycle of the fourth power of a connected graph},
url = {http://eudml.org/doc/29187},
volume = {116},
year = {1991},
}

TY - JOUR
AU - Wisztová, Elena
TI - On a Hamiltonian cycle of the fourth power of a connected graph
JO - Mathematica Bohemica
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 116
IS - 4
SP - 385
EP - 390
AB - In this paper the following theorem is proved: Let $G$ be a connected graph of order $p\ge 4$ and let $M$ be a matching in $G$. Then there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.
LA - eng
KW - Hamiltonian cycle; power of connected graph; matching; powers of graphs; matching in graphs; Hamiltonian cycle; power of connected graph; matching
UR - http://eudml.org/doc/29187
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, On the existence of a 3-factor in the fourth power of a graph, Čas. pěst. mat. 105 (1980), 204-207. (1980) MR0573113
  4. L. Nebeský, Edge-disjoint 1-factors in powers of connected graphs, Czech. Math. J. 34 (109) (1984), 499-505. (1984) MR0764434
  5. L. Nebeský, On a 1-factor of the fourth power of a connected graph, Čas. pěst. mat. 113 (1988), 415-420. (1988) MR0981882
  6. J. Sedláček, Introduction into the Graph Theory, (Czech). Academia nakl. ČSAV, Praha 1981. (1981) 
  7. E. Wisztová, A hamiltonian cycle and a 1-factor in the fourth power of a graph, Čas. pěst. mat. 110 (1985), 403-412. (1985) MR0820332

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