# A special case of Vu's conjecture: Coloring nearly disjoint graphs of bounded maximum degree

@article{Kelly2021ASC, title={A special case of Vu's conjecture: Coloring nearly disjoint graphs of bounded maximum degree}, author={Tom Kelly and Daniela K{\"u}hn and Deryk Osthus}, journal={ArXiv}, year={2021}, volume={abs/2109.11438} }

A collection of graphs is nearly disjoint if every pair of them intersects in at most one vertex. We prove that if G1, . . . , Gm are nearly disjoint graphs of maximum degree at most D, then the following holds. For every fixed C, if each vertex v ∈ ⋃m i=1 V (Gi) is contained in at most C of the graphs G1, . . . , Gm, then the (list) chromatic number of ⋃m i=1 Gi is at most D + o(D). This result confirms a special case of a conjecture of Vu and generalizes Kahn’s bound on the list chromatic…

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