Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: d-cube

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Decomposing complete graphs into cubes

100%

El-Zanati S., Eynden C.

Discussiones Mathematicae Graph Theory

2006

tom 26

nr 1

141-147

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 El-Zanati S.

1 Eynden C.

1 2006

Wyniki wyszukiwania

Decomposing complete graphs into cubes