P. Soorya, K. Augusthy Germina, Naduvath Sudev

A connected, simple graph *G* with vertex set \(V(G)=\{1,2,\ldots ,n\}\) is said to be vertex (*n*, *k*)-choosable, if there exists a collection of subsets \(\left\{ S_k(v)\subseteq V(G): v\in V\right\} \) of cardinality *k*, such that \(S_k(u)\cap S_k(v)=\emptyset \) for all \(uv\in E(G)\), where *k* is a positive integer less than *n*. The maximum value of such *k* is called the vertex choice number of *G*. In this paper, we introduce the notion of \(\alpha \)- choosability of graphs in terms of their vertex (*n*, *k*)-choice number and initiate a study on the structural characteristics of \(\alpha \)-choosable graphs.