TY  - JOUR
ID  - DrgasBurchardt2017
LB  - DrgasBurchardt2017
AU  - Drgas-Burchardt, Ewa
AU  - Drzystek, Agata
TI  - Acyclic sum-list-colouring of grids and other classes of graphs
ST  - Acyclic sum-list-colouring of grids and other classes of graphs
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 4
SP  - 535
EP  - 556
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.4.535
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.4.535
AB  - In this paper we consider list colouring of a graph \(G\) in which the sizes of lists assigned to different vertices can be different. We colour \(G\) from the lists in such a way that each colour class induces an acyclic graph. The aim is to find the smallest possible sum of all the list sizes, such that, according to the rules, \(G\) is colourable for any particular assignment of the lists of these sizes. This invariant is called the \(D_1\)-sum-choice-number of \(G\). In the paper we investigate the \(D_1\)-sum-choice-number of graphs with small degrees. Especially, we give the exact value of the \(D_1\)-sum-choice-number for each grid \(P_n\square P_m\), when at least one of the numbers \(n\), \(m\) is less than five, and for each generalized Petersen graph. Moreover, we present some results that estimate the \(D_1\)-sum-choice-number of an arbitrary graph in terms of the decycling number, other graph invariants and special subgraphs.
KW  - sum-list colouring
KW  - acyclic colouring
KW  - grids
KW  - generalized Petersen graphs
SN  - 1232-9274
ER  -