Geodesic
The ordered set of connected parts of a polygonal graph
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 44-51 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Under a polygonal graph is meant an oriented graph obtained from a cycle by some orientation of its edges. The set of all abstract (i.e. pairwise non-isomorphic) connected parts of a polygonal graph is ordered by graph embedding. Polygonal graphs are characterized for which this ordered set is a lattice. 
@article{ISU_2013_13_2_a6,
     author = {V. N. Salii},
     title = {The ordered set of connected parts of a~polygonal graph},
     journal = {Izvestiya of Saratov University. Mathematics. Mechanics. Informatics},
     pages = {44--51},
     year = {2013},
     volume = {13},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a6/}
}
TY  - JOUR
AU  - V. N. Salii
TI  - The ordered set of connected parts of a polygonal graph
JO  - Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
PY  - 2013
SP  - 44
EP  - 51
VL  - 13
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a6/
LA  - ru
ID  - ISU_2013_13_2_a6
ER  - 
%0 Journal Article
%A V. N. Salii
%T The ordered set of connected parts of a polygonal graph
%J Izvestiya of Saratov University. Mathematics. Mechanics. Informatics
%D 2013
%P 44-51
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a6/
%G ru
%F ISU_2013_13_2_a6
V. N. Salii. The ordered set of connected parts of a polygonal graph. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 13 (2013) no. 2, pp. 44-51. http://geodesic.mathdoc.fr/item/ISU_2013_13_2_a6/

[1] Salii V. N., “Minimal primitive extensions of oriented graphs”, Prikladnaya diskretnaya matematika, 2008, no. 1(1), 116–119

[2] Trotter W. T., Moore J. I., “Some theorems on graphs and posets”, Discrete Math., 15:1 (1976), 79–84 | DOI | MR | Zbl

[3] Jacobson M. S., Kézdy F. E., Seif S., “The poset of connected induced subgraphs of a graph need not be Sperner”, Order, 12:3 (1995), 315–318 | DOI | MR | Zbl

[4] Kézdy A. E., Seif S., “When is a poset isomorphic to the poset of connected induced subgraphs of a graph?”, Southwest J. Pure Appl. Math., 1 (1996), 42–50, (Accessed 28, September, 2012) (Electronic), Available at: http://rattler.cameron.edu/swjpam.html | MR | Zbl

[5] Nieminen J., “The lattice of connected subgraphs of a connected graph”, Comment. Math. Prace Mat., 21:1 (1980), 187–193 | MR

[6] Adams P., Eggleton R. B., MacDougall J. A., “Degree sequences and poset structure of order 9 graphs”, Proc. XXXV Southeast Conf. Comb., Graph Theory and Computing, Congr. Numer., 166, Boca Raton, FL, USA, 2004, 83–95 | MR | Zbl

[7] Leach D., Walsh M., “A characterization of lattice-ordered graphs”, Proc. Integers Conf., Gruyter, N.Y., 2005, 327–332 | MR

[8] Salii V. N., “The system of abstract connected subgraphs of a linear graph”, Prikladnaya diskretnaya matematika, 2012, no. 2(16), 90–94