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Browsing by Subject "sum-list colouring"

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    Item type:Article, Access status: Open Access ,
    Acyclic sum-list-colouring of grids and other classes of graphs
    (Wydawnictwa AGH, 2017) Drgas-Burchardt, Ewa; Drzystek, Agata
    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.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Corrigendum to »Acyclic sum-list-colouring of grids and other classes of graphs« [Opuscula Math. 37, no. 4 (2017), 535-556]
    (Wydawnictwa AGH, 2018) Drgas-Burchardt, Ewa; Drzystek, Agata
    This note provides some minor corrections to the article <a href="https://repo.agh.edu.pl/handle/AGH/112746">Acyclic sum-list-colouring of grids and other classes of graphs, Opuscula Math. 37, no. 4 (2017), 535-556</a>