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In this paper the concepts of Hamilton cycle (HC) and Hamilton path (HP) extendability are introduced. A connected graph Γ is n‐HC‐extendable if it contains a path of length n and if every such path is contained in some Hamilton cycle of Γ. Similarly, Γ is weakly n‐HP‐extendable if it contains a path of length n and if every such path is contained in some Hamilton path of Γ. Moreover, Γ is strongly n...
Let Γ be a connected simple graph, let V(Γ) and E(Γ) denote the vertex-set and the edge-set of Γ, respectively, and let n=|V(Γ)|. For 1≤i≤n, let ei be the element of elementary abelian group Z2n which has 1 in the ith coordinate, and 0 in all other coordinates. Assume that V(Γ)={ei∣1≤i≤n}. We define a set Ω by Ω={ei+ej∣{ei,ej}∈E(Γ)}, and let CayΓ denote the Cayley graph over Z2n with respect to Ω...
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