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A characterization of ( 4 , 2 ) ‐choosable graphs
Author(s) -
Cranston Daniel W.
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22464
Subject(s) - combinatorics , characterization (materials science) , mathematics , conjecture , graph , discrete mathematics , physics , optics
A graph G is ( a , b ) ‐ choosable if given any list assignment L with ∣ L ( v ) ∣ = a for each v ∈ V ( G ) there exists a function φ such that φ ( v ) ⊆ L ( v )and ∣ φ ( v ) ∣ = b for all v ∈ V ( G ) , and whenever vertices x and y are adjacent φ ( x ) ∩ φ ( y ) = ∅ . Meng, Puleo, and Zhu conjectured a characterization of (4,2)‐choosable graphs. We prove their conjecture.