On Edge Exchanges in Hamiltonian Decompositions of Kronecker-product Graphs
نویسندگان
چکیده
Let G be a connected graph on n vertices, and let ; ; and be edge-disjoint cycles in G such that (i) ; (resp. ;) are vertex-disjoint and (ii) jj + jj = jj+ jj = n, where jj denotes the length of. We say that ; ; and yield two edge-disjoint hamiltonian cycles by edge exchanges if the four cycles respectively contain edges e; f; g and h such that each of (? feg) S (? ffg) S fg; hg and (? fgg) S (? fhg) S fe; fg constitutes a hamiltonian cycle in G. We show that if G is a non-bipartite, hamiltonian decomposable graph on an even number of vertices which satisses certain conditions, then Kronecker product of G and K 2 as well as Kronecker product of G and an even cycle admits of a hamiltonian decomposition by means of appropriate edge exchanges among smaller cycles in the product graph. AMS classiication code: 05C45 Key terms: Kronecker product Hamiltonian decomposition Alternate four-cycle Edge exchange
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