Geodesic
The system of abstract connected subgraphs of a~linear graph
Prikladnaâ diskretnaâ matematika, no. 2 (2012), pp. 90-94.

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

A linear graph is a graph obtained from a path by some orientation of its edges. The set of all connected graphs that can be embedded in a given linear graph $L$ is ordered by embedding relation. Conditions on $L$ are found under which this ordered set is a lattice.
Keywords: path, linear graph, abstract subgraph of a graph, ordered set, lattice, binary vector, duality. 
@article{PDM_2012_2_a7,
     author = {V. N. Salii},
     title = {The system of abstract connected subgraphs of a~linear graph},
     journal = {Prikladna\^a diskretna\^a matematika},
     pages = {90--94},
     publisher = {mathdoc},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PDM_2012_2_a7/}
}
TY  - JOUR
AU  - V. N. Salii
TI  - The system of abstract connected subgraphs of a~linear graph
JO  - Prikladnaâ diskretnaâ matematika
PY  - 2012
SP  - 90
EP  - 94
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PDM_2012_2_a7/
LA  - ru
ID  - PDM_2012_2_a7
ER  - 
%0 Journal Article
%A V. N. Salii
%T The system of abstract connected subgraphs of a~linear graph
%J Prikladnaâ diskretnaâ matematika
%D 2012
%P 90-94
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PDM_2012_2_a7/
%G ru
%F PDM_2012_2_a7
V. N. Salii. The system of abstract connected subgraphs of a~linear graph. Prikladnaâ diskretnaâ matematika, no. 2 (2012), pp. 90-94. http://geodesic.mathdoc.fr/item/PDM_2012_2_a7/

[1] Salii V. N., “Minimalnye primitivnye rasshireniya orientirovannykh grafov”, Prikladnaya diskretnaya matematika, 2008, no. 1(1), 116–119

[2] Trotter W. T., Moore J. I., “Some theorems on graphs and posets”, Discr. 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, (Electronic) | 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. 2005, Gruyter, N.Y., 2007, 327–332 | MR | Zbl