Decomposition of complete graphs into factors of diameter two and three

• Autorzy: Damir Vukicević
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

decomposition; graph

Kategorie tematyczne

• 05C70: Factorization, matching, partitioning, covering and packing

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2003
• Tom: 23
• Numer: 1
• Strony: 37-54

Daty

wydano

2003

otrzymano

2001-05-25

poprawiono

2002-09-05

Twórcy

autor

Damir Vukicević

• Department of Mathematics, University of Split, Teslina 12, 21000 Split, Croatia

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgt.1184