Geodesic
Variations on a sufficient condition for Hamiltonian graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 229-240

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Given a 2-connected graph G on n vertices, let G* be its partially square graph, obtained by adding edges uv whenever the vertices u,v have a common neighbor x satisfying the condition N_G(x) ⊆ N_G[u] ∪ N_G[v], where N_G[x] = N_G(x) ∪ x. In particular, this condition is satisfied if x does not center a claw (an induced K_1,3). Clearly G ⊆ G* ⊆ G², where G² is the square of G. For any independent triple X = x,y,z we define
Keywords: cycles, partially square graph, degree sum, independent sets, neighborhood unions and intersections, dual closure 
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     title = {Variations on a sufficient condition for {Hamiltonian} graphs},
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Ainouche, Ahmed; Lapiquonne, Serge. Variations on a sufficient condition for Hamiltonian graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 2, pp. 229-240. http://geodesic.mathdoc.fr/item/DMGT_2007_27_2_a1/