The Hamiltonian cycle and Hamiltonian paths passing through prescribed edges in a star graph with faulty edges
نویسنده
چکیده
Let Fe be the set of faulty edges of Sn and E0 be the edge set of some pairwise vertex-disjoint paths of Sn. All edges of E0 lie on a Hamiltonian cycle of Sn−Fe, if |Fe| ≤ n−3, |E0| ≤ 2n−5−2|Fe| and lie on a Hamiltonian path P (u, v) where d(u, v) is odd, |Fe| ≤ n− 3, |E0| ≤ 2n− 7− 2|Fe| .
منابع مشابه
The Hamiltonian path passing through prescribed edges in a star graph with faulty edges ∗
Let Fe be the set of faulty edges of Sn and E0 be the edge set of some pairwise vertex-disjoint paths of Sn. In [5], the authors showed that E0 lies on a Hamiltonian path P (u, v) of Sn−Fe where d(u, v) is odd, |Fe| ≤ n− 3, |E0| ≤ 2n− 7− 2|Fe|. In this paper we improve the previous result as follows: E0 lies on a Hamiltonian path P (u, v) of Sn − Fe where d(u, v) is odd, Fe ≤ n− 3, |E0| ≤ 2n− 6...
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