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

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

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

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

Edge (m,k)-choosability of graphs

2021 ◽  
Author(s):  
P. Soorya ◽  
K. A. Germina
Keyword(s):  
Connected Graph ◽  
Matching Number ◽  
Graph Theoretic ◽  
Maximum Value ◽  
Choice Number ◽  
The Given ◽  
Simple Connected Graph

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.

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