Geodesic
Hamiltonian completion
Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 87-90.

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This article is a continuation of the work started in [1], where $L(2,1)$-coloring problem is interpreted as optimization task on the set of graph vertices. This approach enabled us to reduce solution of hamiltonian cycle problem to injective $\lambda$-coloring. Here we calculate edge distance from the given graph to the nearest graph containing hamiltonian path, also we construct hamiltonian graphs with at most one extra edge. 
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O. V. Maksimovich; R. I. Tyshkevich. Hamiltonian completion. Trudy Instituta matematiki, Tome 19 (2011) no. 2, pp. 87-90. http://geodesic.mathdoc.fr/item/TIMB_2011_19_2_a9/

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