A d-dimensional hypercube drawing of a graph represents the vertices by distinct points in {0, 1}d, such that the line-segments representing the edges do not cross. We study lower and upper bounds on the minimum number of dimensions in hypercube drawing of a given graph. This parameter turns out to be related to Sidon sets and antimagic injections.

An illustration is given showing the advantage of the definition given by Telyakovskiı̆ for the class introduced by Sidon. It is also verified that if a sequence {an} belongs to the recently defined subclass Sγ of S, γ > 0, then the sequence {nan} belongs to the class S, but the converse statement does not hold.

Let An = ̆ a0 + a1z + · · · + an−1z : a j ∈ {0, 1} ̄ , whose elements are called zeroone polynomials and correspond naturally to the 2n subsets of [n] := {0, 1, . . . , n − 1}. We also let An,m = {α(z) ∈ An : α(1) = m}, whose elements correspond to the `n m ́ subsets of [n] of size m, and let Bn = An+1 \ An, whose elements are the zero-one polynomials of degree exactly n. Many researchers have stu...

We prove a conjecture of Boros, Caro, Füredi and Yuster on the maximum number edges in 2-connected graph without repeated cycle lengths, which is restricted version longstanding problem Erd?s. Our proof together with matched lower bound construction Füuredi show that this can be conceptually reduced to seminal finding Sidon sequences theory.