Geodesic
Cycles of lentgth~9 in the Pancake graph
Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 6, pp. 33-60

Voir la notice de l'article provenant de la source Math-Net.Ru

A cycle $C_l$ of length $l$, where $6\le l\le n!$, can be embedded in the Pancake graph $P_n$, $n\ge3$, that is the Cayley graph on the symmetric group with the generating set of all prefix-reversals. The algebraic characterization of cycles of length six and seven via products of generating elements is known. We continue to study odd cycles. The explicit description of cycles of length nine by means of 10 canonical forms is given. It is also proved that each of vertices of $P_n$, $n\ge4,$ belongs to $\frac{8n^3-45n^2+61n-12}2$ cycles of length nine. In general, there are $O(n!\,n^3)$ different cycles of length nine in the graph. Ill. 5, tab. 1, bibliogr. 10.
Keywords: admissible subgraph, indicator of subgraph's quality, Pareto optimal subgraph. 
@article{DA_2011_18_6_a2,
     author = {E. V. Konstantinova and A. N. Medvedev},
     title = {Cycles of lentgth~9 in the {Pancake} graph},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {33--60},
     publisher = {mathdoc},
     volume = {18},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2011_18_6_a2/}
}
TY  - JOUR
AU  - E. V. Konstantinova
AU  - A. N. Medvedev
TI  - Cycles of lentgth~9 in the Pancake graph
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2011
SP  - 33
EP  - 60
VL  - 18
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2011_18_6_a2/
LA  - ru
ID  - DA_2011_18_6_a2
ER  - 
%0 Journal Article
%A E. V. Konstantinova
%A A. N. Medvedev
%T Cycles of lentgth~9 in the Pancake graph
%J Diskretnyj analiz i issledovanie operacij
%D 2011
%P 33-60
%V 18
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2011_18_6_a2/
%G ru
%F DA_2011_18_6_a2
E. V. Konstantinova; A. N. Medvedev. Cycles of lentgth~9 in the Pancake graph. Diskretnyj analiz i issledovanie operacij, Tome 18 (2011) no. 6, pp. 33-60. http://geodesic.mathdoc.fr/item/DA_2011_18_6_a2/