A matching and a Hamiltonian cycle of the fourth power of a connected graph

Ladislav Nebeský

Mathematica Bohemica (1993)

  • Volume: 118, Issue: 1, page 43-52
  • ISSN: 0862-7959

Abstract

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The following result is proved: Let G be a connected graph of order g e q 4 . Then for every matching M in G 4 there exists a hamiltonian cycle C of G 4 such that E ( C ) ⋂ M = 0 .

How to cite

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Nebeský, Ladislav. "A matching and a Hamiltonian cycle of the fourth power of a connected graph." Mathematica Bohemica 118.1 (1993): 43-52. <http://eudml.org/doc/29166>.

@article{Nebeský1993,
abstract = {The following result is proved: Let $G$ be a connected graph of order $geq 4$. Then for every matching $M$ in $G^4$ there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.},
author = {Nebeský, Ladislav},
journal = {Mathematica Bohemica},
keywords = {matching; factors; Hamiltonian cycles; powers of graphs; connected graph; matching; factors; Hamiltonian cycles; powers of graphs; connected graph},
language = {eng},
number = {1},
pages = {43-52},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A matching and a Hamiltonian cycle of the fourth power of a connected graph},
url = {http://eudml.org/doc/29166},
volume = {118},
year = {1993},
}

TY - JOUR
AU - Nebeský, Ladislav
TI - A matching and a Hamiltonian cycle of the fourth power of a connected graph
JO - Mathematica Bohemica
PY - 1993
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 118
IS - 1
SP - 43
EP - 52
AB - The following result is proved: Let $G$ be a connected graph of order $geq 4$. Then for every matching $M$ in $G^4$ there exists a hamiltonian cycle $C$ of $G^4$ such that $E(C)\bigcap M=0$.
LA - eng
KW - matching; factors; Hamiltonian cycles; powers of graphs; connected graph; matching; factors; Hamiltonian cycles; powers of graphs; connected graph
UR - http://eudml.org/doc/29166
ER -

References

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  1. M. Behzad G. Chartrand, and L. Lesniak-Foster, Graphs & Digraphs, Prindle, Weber L Schmidt, Boston, 1979. (1979) MR0525578
  2. G. Chartrand A. D. PoUmeni, and M. J. Stewart, 10.1016/1385-7258(73)90007-3, Indag. Math. 35 (1973), 228-232. (1973) MR0321809DOI10.1016/1385-7258(73)90007-3
  3. L. Nebeský, On the existence of a 3-factor in the fourth power of graph, Časopis pěst. mat. 105 (1980), 204-207. (1980) MR0573113
  4. L. Nebeský, On a 1-factor of the fourth power of a connected graph, Časopis pěst. mat. 113 (1988), 415-420. (1988) MR0981882
  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. D. P. Sumner, Graphs with 1-factors, Proc. Amer. Math. Soc. 42 (1974), 8-12. (1974) Zbl0293.05157MR0323648
  7. E. Wisztová, A hamiltonian cycle and a 1-factor on the fourth power of a graph, Časopis pěst. mat. 110 (1985), 403-412. (1985) MR0820332
  8. 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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