A local-global principle for vertex-isoperimetric problems
Discrete Mathematics - Kleitman and combinatorics: a celebration
Note: Security number of grid-like graphs
Discrete Applied Mathematics
Concentration on the discrete torus using transportation
Combinatorics, Probability and Computing
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The even discrete torus Tn(k1,...,kn) is the graph on $(\Z/k_1\Z) \times \cdots \times (\Z/k_n\Z)$, where each ki is even and x = (x1,...,xn) is joined to y = (y1,...,yn) if for some i we have xi = yi pm 1 and xj = yj for all $j\ne i$. The main aim of this paper is to describe an ordering on the even discrete torus whose initial segments give a best possible isoperimetric inequality. This extends the partial solution of Bollobás and Leader [SIAM J. Discrete Math., 3 (1990), pp. 32--37] to a problem posed by Wang and Wang [SIAM J. Appl. Math., 33 (1977), pp. 55--59].