- Tytuł:
- Decomposing complete graphs into cubes
- Autorzy:
-
El-Zanati, Saad
Eynden, C. - Powiązania:
- https://bibliotekanauki.pl/articles/743903.pdf
- Data publikacji:
- 2006
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph decomposition
graph factorization
d-cube - Opis:
- This paper concerns when the complete graph on n vertices can be decomposed into d-dimensional cubes, where d is odd and n is even. (All other cases have been settled.) Necessary conditions are that n be congruent to 1 modulo d and 0 modulo $2^d$. These are known to be sufficient for d equal to 3 or 5. For larger values of d, the necessary conditions are asymptotically sufficient by Wilson's results. We prove that for each odd d there is an infinite arithmetic progression of even integers n for which a decomposition exists. This lends further weight to a long-standing conjecture of Kotzig.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 141-147
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł