Ahlswede and Winter [IEEE Trans. Inf. Th. 2002] introduced a Chernoff bound for matrix-valued random variables, which is a non-trivial generalization of the usual Chernoff bound for real-valued random variables. We present an efficient derandomization of their bound using the method of pessimistic estimators (see Raghavan [JCSS 1988]). As a consequence, we derandomize an efficient construction ...

The fractional covering number r* of a hypergraph H (V, E) is defined to be the minimum possible value of ,, v t(x) where ranges over all functions t: V which satisfy ,xe t(x) >= for all edges e e E. In the case of ordinary graphs G, it is known that 2r*(G) is always an integer. By contrast, it is shown (among other things) that for any rational p/q >= 1, there is a 3-uniform hypergraph H with-...

a r t i c l e i n f o a b s t r a c t Keywords: Graph algorithms Simple-path convexity Simple-path convex hull Totally balanced hypergraphs In a connected hypergraph a vertex set X is simple-path convex (sp-convex, for short) if either |X| 1 or X contains every vertex on every simple path between two vertices in X (Faber and Jamison, 1986 [7]), and the sp-convex hull of a vertex set X is the mi...

We study the question of when 0-1 polytopes are normal or, equivalently, having the integer decomposition property. In particular, we shall associate to each 0-1 polytope a labeled hypergraph, and examine the equality between its Ehrhart and polytopal rings via the combinatorial structures of the labeled hypergraph.

The study of perfect state transfer on graphs has attracted a great deal attention during the past ten years because its applications to quantum information processing and computation. Perfect is understood be rare phenomenon. This paper establishes necessary sufficient conditions for bi-Cayley graph having over any given finite abelian group. As corollaries, many known new results are obtained...

We make the following three observations regarding a question popularized by Katznelson: is every subset of $${\mathbb {Z}}$$ which set Bohr recurrence also topological recurrence? (i) If G countable abelian group and $$E\subseteq G$$ an $$I_0$$ set, then $$E-E$$ recurrence. In particular $$\{2^n-2^m : n,m\in {\mathbb {N}}\}$$ (ii) Let {Z}}^{\omega }$$ be direct sum countably many copies with s...

Let d and t be fixed positive integers, and let K t,...,t denote the complete d-partite hypergraph with t vertices in each of its parts, whose hyperedges are the d-tuples of the vertex set with precisely one element from each part. According to a fundamental theorem of extremal hypergraph theory, due to Erdős [7], the number of hyperedges of a d-uniform hypergraph on n vertices that does not co...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

An automorphism α of a Cayley graph Cay(G,S) of a group G with connection set S is color-preserving if α(g, gs) = (h, hs) or (h, hs−1) for every edge (g, gs) ∈ E(Cay(G,S)). If every color-preserving automorphism of Cay(G,S) is also affine, then Cay(G,S) is a CCA (Cayley color automorphism) graph. If every Cayley graph Cay(G,S) is a CCA graph, then G is a CCA group. Hujdurović, Kutnar, D.W. Morr...

The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.