Decomposition of cartesian products of regular graphs into isomorphic trees
نویسندگان
چکیده
We extend the ideas of Snevily and Avgustinovitch to enlarge the families of 2mregular graphs and m-regular bipartite graphs that are known to decompose into isomorphic copies of a tree T with m edges. For example, consider r1, . . . , rk with ∑k i=1 ri = m. If T has a k-edge-coloring with ri edges of color i such that every path in T uses some color once or twice, then every cartesian product of graphs G1, . . . , Gk such that Gi is 2ri-regular for 1 ≤ i ≤ k decomposes into copies of T .
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