Abstract Let 𝐺 be a graph with 𝑛 vertices and 𝑆 = 𝕂[𝑥₁, …, 𝑥𝑛] be the polynomial ring in 𝑛 variables over a field 𝕂. Assume that 𝐽(𝐺) is the cover ideal of 𝐺 and 𝐽(𝐺)⁽𝑘⁾ is its 𝑘-th ...

Abstract Forty years ago, Kleitman considered the numbers of crossings in good planar drawings of the complete bipartite graph ${K_{m,n}}$. Among other things, he ...