Let T be a tree with m edges. It was conjectured that every m-regular bipartite graph can be decomposed into edge-disjoint copies of T. In this paper, we prove that every 6-regular bipartite graph can be decomposed into edge-disjoint paths with 6 edges. As a consequence, every 6-regular bipartite graph on n vertices can be decomposed into \(\frac{n}{2}\) paths, which is related to the well-known Gallai’s Conjecture: every connected graph on n vertices can be decomposed into at most \(\frac{n+1}{2}\) paths.

中文翻译：

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6-正则二分图分解为长度为6的路径

令T为具有m个边的树。据推测，每个m-正则二分图都可以分解为T的边不相交的副本。在本文中，我们证明了每个6-正则二分图都可以分解为具有6条边的边不相交的路径。结果，可以将n个顶点上的每个6正则二分图分解为\（\ frac {n} {2} \）路径，这与众所周知的加莱猜想有关：n个顶点上的每个连通图都可以最多分解为\（\ frac {n + 1} {2} \）条路径。