Geodesic
Sum list coloring \(2\times n\) arrays
The electronic journal of combinatorics, Tome 9 (2002)
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A graph is $f$-choosable if for every collection of lists with list sizes specified by $f$ there is a proper coloring using colors from the lists. The sum choice number is the minimum over all choosable functions $f$ of the sum of the sizes in $f$. We show that the sum choice number of a $2 \times n$ array (equivalent to list edge coloring $K_{2,n}$ and to list vertex coloring the cartesian product $K_2 \square K_n$) is $n^2 + \lceil 5n/3 \rceil$.
DOI : 10.37236/1669
Classification : 05C15
Mots-clés : sum choice number 
@article{10_37236_1669,
     author = {Garth Isaak},
     title = {Sum list coloring \(2\times n\) arrays},
     journal = {The electronic journal of combinatorics},
     year = {2002},
     volume = {9},
     doi = {10.37236/1669},
     zbl = {1003.05041},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1669/}
}
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%A Garth Isaak
%T Sum list coloring \(2\times n\) arrays
%J The electronic journal of combinatorics
%D 2002
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Garth Isaak. Sum list coloring \(2\times n\) arrays. The electronic journal of combinatorics, Tome 9 (2002). doi: 10.37236/1669

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