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Note on cyclic decompositions of complete bipartite graphs into cubes

100%

Fronček D.

Discussiones Mathematicae Graph Theory

1999

tom 19

nr 2

219-227

So far, the smallest complete bipartite graph which was known to have a cyclic decomposition into cubes $Q_d$ of a given dimension d was $K_{d2^{d-1}, d2^{d-2}}$. We improve this result and show that also $K_{d2^{d-2}, d2^{d-2}}$ allows a cyclic decomposition into $Q_d$. We also present a cyclic factorization of $K_{8,8}$ into Q₄.

Lattice-Like Total Perfect Codes

100%

Araujo C., Dejter I.

Discussiones Mathematicae Graph Theory

2014

tom 34

nr 1

57-74

A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ) formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.

Duality for some free modes

75%

Pszczoła K., Romanowska A., Smith J.

Discussiones Mathematicae - General Algebra and Applications

2003

tom 23

nr 1

45-61

The paper establishes a duality between a category of free subreducts of affine spaces and a corresponding category of generalized hypercubes with constants. This duality yields many others, in particular a duality between the category of (finitely generated) free barycentric algebras (simplices of real affine spaces) and a corresponding category of hypercubes with constants.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Discussiones Mathematicae - General Algebra and Applications

1 Araujo C.

1 Dejter I.

1 Fronček D.

1 Pszczoła K.

1 Romanowska A.

1 Smith J.

1 2014

1 2003

1 1999

Wyniki wyszukiwania

Note on cyclic decompositions of complete bipartite graphs into cubes

Lattice-Like Total Perfect Codes

Duality for some free modes