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ENDM
2007
14 years 11 months ago
2007
Given a metric d on a permutation group G, the corresponding weight problem is to decide whether there exists an element g ∈ G such that d(g, e) = k for some k ∈ N. In this pa...
ENDM
2007
14 years 11 months ago
2007
We show that the number of maximal sum-free subsets of {1, 2, . . . , n} is at most 23n/8+o(n) . We also show that 20.406n+o(n) is an upper bound on the number of maximal product-...
ENDM
2007
14 years 11 months ago
2007
For any finite abelian group G and any subset S ⊆ G, we determine the connectivity of the addition Cayley graph induced by S on G. Moreover, we show that if this graph is not c...
ENDM
2007
14 years 11 months ago
2007
In 1977, Wegner conjectured that the chromatic number of the square of every planar graph G with maximum degree ∆ ≥ 8 is at most 3
ENDM
2007
14 years 11 months ago
2007
Kreweras’ conjecture [9] asserts that every perfect matching of the hypercube Qd can be extended to a Hamiltonian cycle of Qd. We [5] proved this conjecture but here we present ...