List Colouring Trees in Logarithmic Space

Abstract

We show that List Colouring can be solved on n -vertex trees by a deterministic Turing machine using O (log n ) bits on the worktape. Given an n -vertex graph G = ( V, E ) and a list L ( v ) ⊆ { 1 , . . . , n } of available colours for each v ∈ V , a list colouring for G is a proper colouring c such that c ( v ) ∈ L ( v ) for all v .