摘要：Given a hypergraph H, the conflict-free colouring problem is to colour vertices of H using minimum colours so that in every hyperedge e of H, there is a vertex whose colour is different from that of all other vertices in e. Our results are on a variant of the conflict-free colouring problem considered by Cheilaris et al.[Cheilaris et al., 2014], known as the 1-Strong Conflict-Free (1-SCF) colouring problem, for which they presented a polynomial time 2-approximation algorithm for interval hypergraphs. We show that an optimum 1-SCF colouring for interval hypergraphs can be computed in polynomial time. Our results are obtained by considering a different view of conflict-free colouring which we believe could be useful in general. For interval hypergraphs, this different view brings a connection to the theory of perfect graphs which is useful in coming up with an LP formulation to select the vertices that could be coloured to obtain an optimum conflict-free colouring. The perfect graph connection again plays a crucial role in finding a minimum colouring for the vertices selected by the LP formulation.
