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The anti-apoptotic protein MCL-1 is a key regulator of cancer cell survival and a known resistance factor for small-molecule BCL-2 family inhibitors such as ABT-263 (navitoclax), making it an attractive therapeutic target. However, directly inhibiting this target requires the disruption of high-affinity protein-protein interactions, and therefore designing… (More)
It was proved by Fronček, Jerebic, Klavžar, and Kovář that if a complete bi-partite graph K n,n with a perfect matching removed can be covered by k bicliques, then n ≤ k k 2. We give a slightly simplified proof and we show that the result is tight. Moreover we use the result to prove analogous bounds for coverings of some other classes of graphs by… (More)
The strong isometric dimension of a graph G is the least number k such that G isometrically embeds into the strong product of k paths. Using Sperner's Theorem, the strong isometric dimension of the Hamming graphs K 2 K n is determined.
Let G(V, E) be a graph and λ be a bijection from the set V ∪ E to the set of the first |V | + |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s, d)-vertex antimagic total (VAT) labeling if… (More)