We show that cr(G) ≤ 2 iocr(G) 2 settling an open problem of Pach and T´oth [4, 1]. Moreover, iocr(G) = cr(G) if iocr(G) ≤ 2. 1 Crossing Numbers Pach and T´oth point out in ...
Michael J. Pelsmajer, Marcus Schaefer, Daniel Stef...
A succinct series expression is derived for describing the limit distribution of the number of times r consecutive elements are all records (in a sequence of independent and ident...
For each k 2, let k (0, 1) be the largest number such that there exist k-uniform hypergraphs on n vertices with independent neighborhoods and (k + o(1)) n k edges as n . We pro...
Tom Bohman, Alan M. Frieze, Dhruv Mubayi, Oleg Pik...
The achromatic number (G) of a graph G = (V, E) is the maximum k such that V has a partition V1, V2, . . . , Vk into independent sets, the union of no pair of which is independent...
We prove that if G = (VG, EG) is a finite, simple, and undirected graph with κ components and independence number α(G), then there exist a positive integer k ∈ N and a functi...