Authors: Z.-C. Chen, H.-C. Lee Title: Decomposing the complete graph into Hamiltonian paths (cycles) and 3-stars Source: Discussiones Mathematicae Graph Theory Received 12.01.2018, Revised 14.05.2018, Accepted 14.05.2018, doi: 10.7151/dmgt.2153 | |
Abstract: Let H be a graph. A decomposition of H is a set of edge-disjoint subgraphs of H whose union is H. A Hamiltonian path (respectively, cycle) of H is a path (respectively, cycle) {that} contains every vertex of H exactly once. A k-star, denoted by S_{k}, is a star with k edges. In this paper, we give necessary and sufficient conditions for decomposing the complete graph into α copies of Hamiltonian path (cycle) and β copies of S_{3}. | |
Keywords: decomposition, complete graph, Hamiltonian path, Hamiltonian cycle, star | |
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