Edge (m,k)-choosability of graphs.

Let G = (V , E) be a simple, connected graph of order n and size m. Then, G = (V , E) is said to be edge (m , k) -choosable, if there exists a collection of subsets of the edge set, { S k (e) : e ∈ E (G) } of cardinality k , such that S k (e 1) ∩ S k (e 2) = ∅ , whenever e 1 and e 2 are incident. This paper initiates a study on edge (m , k) -choosability of certain fundamental classes of graphs and determines the maximum value of k , for which the given graph G is edge (m , k) -choosable. Also, in this paper, the relation between edge choice number and other graph theoretic parameters is discussed and we have given a conjecture on the relation between edge choice number and matching number of a graph. [ABSTRACT FROM AUTHOR]