On r -extendability of the hypercube Q n

Nirmala B. Limaye; Dinesh G. Sarvate

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 3, page 249-255
  • ISSN: 0862-7959

Abstract

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A graph having a perfect matching is called r -extendable if every matching of size r can be extended to a perfect matching. It is proved that in the hypercube Q n , a matching S with | S | ≤ n can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, Q n is r -extendable for every r with 1 ≤ r ≤ n - 1 .

How to cite

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Limaye, Nirmala B., and Sarvate, Dinesh G.. "On $r$-extendability of the hypercube $Q_n$." Mathematica Bohemica 122.3 (1997): 249-255. <http://eudml.org/doc/248123>.

@article{Limaye1997,
abstract = {A graph having a perfect matching is called $r$-extendable if every matching of size $r$ can be extended to a perfect matching. It is proved that in the hypercube $Q_n$, a matching $S$ with $ |S|\le n$ can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, $Q_n$ is $r$-extendable for every $r$ with $1\le r\le n-1.$},
author = {Limaye, Nirmala B., Sarvate, Dinesh G.},
journal = {Mathematica Bohemica},
keywords = {hypercube; perfect matching; 1-factor; $r$-extendability; 1-factor; -extendability; hypercube; perfect matching},
language = {eng},
number = {3},
pages = {249-255},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On $r$-extendability of the hypercube $Q_n$},
url = {http://eudml.org/doc/248123},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Limaye, Nirmala B.
AU - Sarvate, Dinesh G.
TI - On $r$-extendability of the hypercube $Q_n$
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 3
SP - 249
EP - 255
AB - A graph having a perfect matching is called $r$-extendable if every matching of size $r$ can be extended to a perfect matching. It is proved that in the hypercube $Q_n$, a matching $S$ with $ |S|\le n$ can be extended to a perfect matching if and only if it does not saturate the neighbourhood of any unsaturated vertex. In particular, $Q_n$ is $r$-extendable for every $r$ with $1\le r\le n-1.$
LA - eng
KW - hypercube; perfect matching; 1-factor; $r$-extendability; 1-factor; -extendability; hypercube; perfect matching
UR - http://eudml.org/doc/248123
ER -

References

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  1. N. B. Limaye, Mulupury Shanthi C. Rao, On 2-extendability of generalized Petersen graphs, Math. Bohem. 121 (1996), 77-81. (1996) MR1388178
  2. Tsuyoshi Nishimura, A theorem on n-extendable graphs, Ars Combinatoria 38 (1994), 3-5. (1994) MR1310401
  3. M. D. Plummer, 10.1016/0012-365X(80)90037-0, Discrete Math. 31 (1980), 201-210. (1980) Zbl0442.05060MR0583220DOI10.1016/0012-365X(80)90037-0
  4. G. Schrag, L. Cammack, 10.1016/0012-365X(89)90174-X, Discrete Math. 78 (1989), 169-177. (1989) Zbl0723.05086MR1020660DOI10.1016/0012-365X(89)90174-X

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