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In this paper we investigate the problem of computing two parameters of a graph: the Total Interval Number TIN(G), and the Hamiltonian Completion Number HCN(G). We show that in case of a triangle-free graph these two parameters (TIN(G) and HCN(L(G)), where L(G) is the line graph of G) are related by a simple formula. We use this relationship to find a polynomial algorithm which determines TIN(G),...
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