Asymptotically good local list edge colourings
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Abstract
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.
Article Details
How to Cite
Bonamy, M., Delcourt, M., Lang, R., & Postle, L.
(2019).
Asymptotically good local list edge colourings.
Acta Mathematica Universitatis Comenianae, 88(3), 489-494.
Retrieved from http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1245/685
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Section
EUROCOMB 2019