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On $$\alpha$$ α -Vertex Choosability of Graphs
National Academy Science Letters  (IF0.788),  Pub Date : 2020-07-30, DOI: 10.1007/s40009-020-01006-x
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 (nk)-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 (nk)-choice number and initiate a study on the structural characteristics of $$\alpha$$-choosable graphs.