Lower bounds on the sum choice number of a graph

2016 ◽  
Vol 53 ◽  
pp. 421-431 ◽  
Author(s):  
Jochen Harant ◽  
Arnfried Kemnitz
Keyword(s):  
Lower Bounds ◽  
Choice Number ◽  
Sum Choice Number

scholarly journals Sum choice number of generalizedθ-graphs

2017 ◽  
Vol 340 (11) ◽  
pp. 2633-2640 ◽  
Author(s):  
Christoph Brause ◽  
Arnfried Kemnitz ◽  
Massimiliano Marangio ◽  
Anja Pruchnewski ◽  
Margit Voigt
Keyword(s):  
Choice Number ◽  
Sum Choice Number

scholarly journals The Interactive Sum Choice Number of Graphs

2017 ◽  
Vol 61 ◽  
pp. 139-145
Author(s):  
Marthe Bonamy ◽  
Kitty Meeks
Keyword(s):  
Choice Number ◽  
Sum Choice Number

scholarly journals The interactive sum choice number of graphs

2021 ◽  
Vol 292 ◽  
pp. 72-84
Author(s):  
Marthe Bonamy ◽  
Kitty Meeks
Keyword(s):  
Choice Number ◽  
Sum Choice Number

Bounds for the sum choice number

2017 ◽  
Vol 63 ◽  
pp. 49-58
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio ◽  
Margit Voigt
Keyword(s):  
Choice Number ◽  
Sum Choice Number

Comparison of sum choice number with chromatic sum

2021 ◽  
Vol 344 (7) ◽  
pp. 112391
Author(s):  
Arnfried Kemnitz ◽  
Massimiliano Marangio ◽  
Zsolt Tuza ◽  
Margit Voigt
Keyword(s):  
Chromatic Sum ◽  
Choice Number ◽  
Sum Choice Number

scholarly journals The sum choice number of P3□Pn

2012 ◽  
Vol 160 (7-8) ◽  
pp. 1126-1136 ◽  
Author(s):  
Brian Heinold
Keyword(s):  
Choice Number ◽  
Sum Choice Number

scholarly journals Sum List Coloring $2 \times n$ Arrays

10.37236/1669 ◽  
2002 ◽  
Vol 9 (1) ◽  
Author(s):  
Garth Isaak
Keyword(s):  
Cartesian Product ◽  
Edge Coloring ◽  
Vertex Coloring ◽  
List Coloring ◽  
Proper Coloring ◽  
List Edge Coloring ◽  
Choice Number ◽  
Sum Choice Number

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 $n^2 + \lceil 5n/3 \rceil$.

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