Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: graph factorization

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.

Cyclic decompositions of complete graphs into spanning trees

100%

Froncek D.

Discussiones Mathematicae Graph Theory

2004

tom 24

nr 2

345-353

We examine decompositions of complete graphs with an even number of vertices, $K_{2n}$, into n isomorphic spanning trees. While methods of such decompositions into symmetric trees have been known, we develop here a more general method based on a new type of vertex labelling, called flexible q-labelling. This labelling is a generalization of labellings introduced by Rosa and Eldergill.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 El-Zanati S.

1 Eynden C.

1 Froncek D.

1 2006

1 2004

Wyniki wyszukiwania

Decomposing complete graphs into cubes

Cyclic decompositions of complete graphs into spanning trees