Geodesic
Open packing number for some classes of perfect graphs
Ural mathematical journal, Tome 6 (2020) no. 2, pp. 38-43 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Let $G$ be a graph with the vertex set $V(G)$. A subset $S$ of $V(G)$ is an open packing set of $G$ if every pair of vertices in $S$ has no common neighbor in $G.$ The maximum cardinality of an open packing set of $G$ is the open packing number of $G$ and it is denoted by $\rho^o(G)$. In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, $\{P_4, C_4\}$-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.
Keywords: open packing number, 2-packing number, perfect graphs, trestled graphs. 
@article{UMJ_2020_6_2_a3,
     author = {K. Raja Chandrasekar and S. Saravanakumar},
     title = {Open packing number for some classes of perfect graphs},
     journal = {Ural mathematical journal},
     pages = {38--43},
     year = {2020},
     volume = {6},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/}
}
TY  - JOUR
AU  - K. Raja Chandrasekar
AU  - S. Saravanakumar
TI  - Open packing number for some classes of perfect graphs
JO  - Ural mathematical journal
PY  - 2020
SP  - 38
EP  - 43
VL  - 6
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/
LA  - en
ID  - UMJ_2020_6_2_a3
ER  - 
%0 Journal Article
%A K. Raja Chandrasekar
%A S. Saravanakumar
%T Open packing number for some classes of perfect graphs
%J Ural mathematical journal
%D 2020
%P 38-43
%V 6
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/
%G en
%F UMJ_2020_6_2_a3
K. Raja Chandrasekar; S. Saravanakumar. Open packing number for some classes of perfect graphs. Ural mathematical journal, Tome 6 (2020) no. 2, pp. 38-43. http://geodesic.mathdoc.fr/item/UMJ_2020_6_2_a3/

[1] Aparna Lakshmanan S., Vijayakumar A., “The $\langle t\rangle$-property of some classes of graphs”, Discrete Math., 309:1 (2009), 259–263 | DOI | MR | Zbl

[2] Berge C., The Theory of Graphs and its Applications, Methuen, London, 1962, 257 pp. | MR | Zbl

[3] Berge C., Graphs and Hypergraphs, North-Holland, London, 1973, 528 pp. | MR | Zbl

[4] Chartrand G., Lesniak L., Graphs and Digraphs, $4^{th}$, Chapman and Hall/CRC, London, 2005, 386 pp. | MR | Zbl

[5] Chudnovsky M., Robertson N., Seymour P., Thomas R., “The strong perfect graph theorem”, Ann. Math., 164:1 (2006), 51—229 | DOI | MR | Zbl

[6] Fellows M., Fricke G., Hedetniemi S., Jacobs D., “The private neighbor cube”, SIAM J. Discrete Math., 7:1 (1994), 41–47 | DOI | MR | Zbl

[7] Fisher D. C., Mckenna P. A., Boyer E. D., “Hamiltonicity, diameter, domination, packing and biclique partitions of Mycielski's graphs”, Discrete Appl. Math., 84:1–3 (1998), 93–105 | DOI | MR | Zbl

[8] Henning M. A., Slater P. J., “Open packing in graphs”, J. Combin. Math. Combin. Comput., 29 (1999), 3–16 | MR | Zbl

[9] Hougardy S., “Classes of perfect graphs”, Discrete Math., 306:19-20 (2006), 2529–2571 | DOI | MR | Zbl

[10] Lovász L., “Normal hypergraphs and the perfect graph conjecture”, Discrete Math., 2:3 (1972), 253–267 | DOI | MR | Zbl

[11] Meir A., Moon J. W., “Relations between packing and covering numbers of a tree”, Pacific J. Math., 61:1 (1975), 225–233 https://projecteuclid.org/euclid.pjm/1102868240 | DOI | MR | Zbl

[12] Mojdeh D. A., Samadi B., Khodkar A. and Golmohammadi H. R., “On the packing numbers in graphs”, Australas. J. Combin., 2018 Vol. 71, no. 3, 468–475 https://ajc.maths.uq.edu.au/pdf/71/ajc_v71_p468.pdf | MR | Zbl

[13] Mycielski J., “Sur le coloriage des graphes”, Colloq. Math., 3 (1955), 161–162 | DOI | MR | Zbl

[14] Sahul Hamid I., Saravanakumar S., “Packing parameters in graphs”, Discuss. Math. Graph Theory, 35 (2015), 5–16 | DOI | MR | Zbl

[15] Seinsche D., “On a property of the class of $n$-colorable graphs”, J. Combin. Theory Ser. B, 16:2 (1974), 191–193 | DOI | MR | Zbl