Edge (m,k)-choosability of graphs
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Published:2021-10-27
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Volume:
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Soorya P.1,
Germina K. A.1
Affiliation:
1. Department of Mathematics, Central University of Kerala, Kasaragod 671316, Kerala, India
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.
Funder
Council of Scientific and Industrial Research, India
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics