Every 2-choosable graph is circular consecutive 2-choosable

Suppose G is a graph, r is a positive real number and S(r) is a circle of perimeter r. For a positive real number t ≤ r, a (t, r)circular consecutive colour-list assignment L is a mapping that assigns to each vertex v of G an interval L(v) of S(r) of length t. A circular L-colouring of G is a mapping f : V (G) → S(r) such that for each vertex v, f(v) ∈ L(v) and for each edge uv, the distance between f(u) and f(v) in S(r) is at least 1. A graph G is called circular consecutive t-choosable if for any r ≥ χc(G), for any (t, r)-circular consecutive colour-list assignment L, G has a circular L-colouring. This paper proves that every 2-choosable graph is circular consecutive 2-choosable.