Geodesic
Decomposition of complete graphs into factors of diameter two and three
Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 37-54

Voir la notice de l'article provenant de la source Library of Science

We analyze a minimum number of vertices of a complete graph that can be decomposed into one factor of diameter 2 and k factors of diameter at most 3. We find exact values for k ≤ 4 and the asymptotic value of the ratio of this number and k when k tends to infinity. We also find the asymptotic value of the ratio of the number of vertices of the smallest complete graph that can be decomposed into p factors of diameter 2 and k factors of diameter 3 and number k when p is fixed.
Keywords: decomposition, graph 
Vukicević, Damir. Decomposition of complete graphs into factors of diameter two and three. Discussiones Mathematicae. Graph Theory, Tome 23 (2003) no. 1, pp. 37-54. http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a2/
@article{DMGT_2003_23_1_a2,
     author = {Vukicevi\'c, Damir},
     title = {Decomposition of complete graphs into factors of diameter two and three},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {37--54},
     year = {2003},
     volume = {23},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a2/}
}
TY  - JOUR
AU  - Vukicević, Damir
TI  - Decomposition of complete graphs into factors of diameter two and three
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2003
SP  - 37
EP  - 54
VL  - 23
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a2/
LA  - en
ID  - DMGT_2003_23_1_a2
ER  - 
%0 Journal Article
%A Vukicević, Damir
%T Decomposition of complete graphs into factors of diameter two and three
%J Discussiones Mathematicae. Graph Theory
%D 2003
%P 37-54
%V 23
%N 1
%U http://geodesic.mathdoc.fr/item/DMGT_2003_23_1_a2/
%G en
%F DMGT_2003_23_1_a2

[1] B. Bollobás, Extremal Graph Theory (Academic Press, London, 1978).

[2] J. Bosák, Disjoint factors of diameter two in complete graphs, J. Combin. Theory (B) 16 (1974) 57-63, doi: 10.1016/0095-8956(74)90095-1.

[3] J. Bosák, A. Rosa and S. Znám, On decompositions of complete graphs into factors with given diameters, in: Proc. Colloq. Tihany (Hung), (1968) 37-56.

[4] D. Palumbíny, On decompositions of complete graphs into factors with equal diameters, Bollettino U.M.I. (4) 7 (1973) 420-428.

[5] P. Hrnciar, On decomposition of complete graphs into three factors with given diameters, Czechoslovak Math. J. 40 (115) (1990) 388-396.

[6] N. Sauer, On factorization of complete graphs into factors of diameter two, J. Combin. Theory 9 (1970) 423-426, doi: 10.1016/S0021-9800(70)80096-5.

[7] S. Znám, Decomposition of complete graphs into factors of diameter two, Math. Slovaca 30 (1980) 373-378.

[8] S. Znám, On a conjecture of Bollobás and Bosák, J. Graph Theory 6 (1982) 139-146.