A Construction of Uniquely C 4 -free colourable Graphs

Abstract
An F-free colouring of a graph G is a partition {V1,V2,…,Vn} of the vertex set V(G) of G such that F is not an induced subgraph of G[Vi] for each i. A graph is uniquely F-free colourable if any two .F-free colourings induce the same partition of V(G). We give a constructive proof that uniquely C4-free colourable graphs exist.
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