A note on choosability with defect 1 of graphs on surfaces

Vida Dujmović, Djedjiga Outioua

This note proves that every graph of Euler genus $\mu$ is $\lceil 2+\sqrt{3\mu +3}\rceil$--choosable with defect 1 (that is, clustering 2). Thus, allowing defect as small as 1 redu…