# Decomposition of complete graphs into factors of diameter two and three

Discussiones Mathematicae Graph Theory (2003)

- Volume: 23, Issue: 1, page 37-54
- ISSN: 2083-5892

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topDamir Vukicević. "Decomposition of complete graphs into factors of diameter two and three." Discussiones Mathematicae Graph Theory 23.1 (2003): 37-54. <http://eudml.org/doc/270782>.

@article{DamirVukicević2003,

abstract = {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.},

author = {Damir Vukicević},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {decomposition; graph; graph decomposition; graph diameter},

language = {eng},

number = {1},

pages = {37-54},

title = {Decomposition of complete graphs into factors of diameter two and three},

url = {http://eudml.org/doc/270782},

volume = {23},

year = {2003},

}

TY - JOUR

AU - Damir Vukicević

TI - Decomposition of complete graphs into factors of diameter two and three

JO - Discussiones Mathematicae Graph Theory

PY - 2003

VL - 23

IS - 1

SP - 37

EP - 54

AB - 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.

LA - eng

KW - decomposition; graph; graph decomposition; graph diameter

UR - http://eudml.org/doc/270782

ER -

## References

top- [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. Zbl0256.05117
- [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. Zbl0159.54203
- [4] D. Palumbíny, On decompositions of complete graphs into factors with equal diameters, Bollettino U.M.I. (4) 7 (1973) 420-428. Zbl0264.05124
- [5] P. Hrnciar, On decomposition of complete graphs into three factors with given diameters, Czechoslovak Math. J. 40 (115) (1990) 388-396. Zbl0748.05075
- [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. Zbl0213.51004
- [7] S. Znám, Decomposition of complete graphs into factors of diameter two, Math. Slovaca 30 (1980) 373-378. Zbl0462.05052
- [8] S. Znám, On a conjecture of Bollobás and Bosák, J. Graph Theory 6 (1982) 139-146. Zbl0497.05049

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