Find Paper, Faster
Example:10.1021/acsami.1c06204 or Chem. Rev., 2007, 107, 2411-2502
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.