A combinatorial approach for Keller's conjecture |
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Authors: | K Corrádi S Szabó |
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Institution: | (1) Dept. of computer Techn, Eötvös Loránd univ, Muzeum KRT. 6-8, H-1088 Budapest, Hungary;(2) Dept. of civil engineering math, Tech. univ. Budapest, Stoczek U. 2, H-1111 Budapest, Hungary |
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Abstract: | The statement, that in a tiling by translates of ann-dimensional cube there are two cubes having common (n-1)-dimensional faces, is known as Keller's conjecture. We shall prove that there is a counterexample for this conjecture if and only if the following graphs
n
has a 2
n
size clique. The 4
n
vertices of
n
aren-tuples of integers 0, 1, 2, and 3. A pair of thesen-tuples are adjacent if there is a position at which the difference of the corresponding components is 2 modulo 4 and if there is a further position at which the corresponding components are different. We will give the size of the maximal cliques of
n
forn 5. |
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Keywords: | Primary 10E30 Secondary 20K01 |
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