Abstract
Let [Formula: see text] be a simple, connected graph of order [Formula: see text] and size [Formula: see text] Then, [Formula: see text] is said to be edge [Formula: see text]-choosable, if there exists a collection of subsets of the edge set, [Formula: see text] of cardinality [Formula: see text] such that [Formula: see text] whenever [Formula: see text] and [Formula: see text] are incident. This paper initiates a study on edge [Formula: see text]-choosability of certain fundamental classes of graphs and determines the maximum value of [Formula: see text] for which the given graph [Formula: see text] is edge [Formula: see text]-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.
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