首页> 外文期刊>The Journal of Combinatorial Mathematics and Combinatorial Computing >Decomposition of complete tripartite graphs into gregarious 3-paths and 6-cycles
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Decomposition of complete tripartite graphs into gregarious 3-paths and 6-cycles

机译:将完整的三方图分解为合群的3路径和6循环

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In this paper, we refer to a decomposition of a tripartite graph into paths of length 3, or into 6-cycles, as gregarious if each subgraph has at least one vertex in each of the three partite sets. For a tripartite graph to have a 6-cycle decomposition it is straightforward to see that all three parts must have even size. Here we provide a gregarious decomposition of a complete tripartite graph K(r, s, t) into paths of length 3, and thus of K(2r, 2s, 2t) into gregarious 6-cycles, in all possible cases, when the straightforward necessary conditions on r,s,t are satisfied.
机译:在本文中,如果每个子图在三个部分集中都具有至少一个顶点,则将三方图分解为长度为3或6个循环的路径是合群的。为了使三重图具有6个循环的分解,可以很容易地看出所有三个部分都必须具有偶数大小。在这里,我们将完整的三方图K(r,s,t)分解成长度为3的路径,从而将K(2r,2s,2t)分解成合群的6个循环,在所有可能的情况下,满足r,s,t的必要条件。

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