%A Bonamy, Marthe
%A Delcourt, Michelle
%A Lang, Richard
%A Postle, Luke
%D 2019
%T Asymptotically good local list edge colourings
%K
%X We study list edge colourings under local conditions. Our main result is an analogue of Kahn's theorem in this setting. More precisely, we show that, for a simple graph $G$ with sufficiently large maximum degree $\Delta$ and minimum degree $\delta \geq \ln^{25} \Delta$, the following holds. Suppose that lists of colours $L(e)$ are assigned to the edges of $G$, such that, for each edge $e=uv$, $$|L(e)| \geq (1+o(1)) \cdot \max\left\{\deg(u),\deg(v)\right\}.$$ Then there is an $L$-edge-colouring of $G$. We also provide extensions of this result for hypergraphs and correspondence colourings, a generalization of list colouring.
%U http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1245
%J Acta Mathematica Universitatis Comenianae
%0 Journal Article
%P 489-494%V 88
%N 3
%@ 0862-9544
%8 2019-07-26