1 research outputs found
Adaptable and conflict colouring multigraphs with no cycles of length three or four
The adaptable choosability of a multigraph , denoted ,
is the smallest integer such that any edge labelling, , of and
any assignment of lists of size to the vertices of permits a list
colouring, , of such that there is no edge where . Here we show that for a multigraph with maximum
degree and no cycles of length 3 or 4, . Under natural restrictions we can
show that the same bound holds for the conflict choosability of , which is a
closely related parameter defined by Dvo\v{r}\'ak, Esperet, Kang and Ozeki
[arXiv:1803.10962].Comment: 30 page