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Choosability with Separation of Complete Multipartite Graphs and Hypergraphs
Author(s) -
Füredi Zoltán,
Kostochka Alexandr,
Kumbhat Mohit
Publication year - 2014
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.21754
Subject(s) - multipartite , mathematics , combinatorics , hypergraph , integer (computer science) , discrete mathematics , computer science , physics , quantum mechanics , quantum entanglement , quantum , programming language
Abstract For a hypergraph G and a positive integer s , letχ ℓ ( G , s )be the minimum value of l such that G is L ‐colorable from every list L with | L ( v ) | = l for each v ∈ V ( G ) and | L ( u ) ∩ L ( v ) | ≤ s for all u , v ∈ e ∈ E ( G ) . This parameter was studied by Kratochvíl, Tuza, and Voigt for various kinds of graphs. Using randomized constructions we find the asymptotics ofχ ℓ ( G , s )for balanced complete multipartite graphs and for complete k ‐partite k ‐uniform hypergraphs.