Counting cocircuits and convex two-colourings is #P-complete

We prove that the problem of counting the number of colourings of the vertices of a graph with at most two colours, such that the colour classes induce connected subgraphs is #P-complete. We also show that the closely related problem of counting the number of cocircuits of a graph is #P-complete.

Country

United Kingdom

Related Organizations

Brunel University London
United Kingdom

Keywords

Graph colouring, #P-complete, Cocircuits, Convex colouring

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