Path decompositions and perfect path double covers
نویسندگان
چکیده
We consider edge-decompositions of regular graphs into isomorphic paths. An m-PPD (perfect path decomposition) is a decomposition of a graph into paths of length m such that every vertex is an end of exactly two paths. An m-PPDC (perfect path double cover) is a covering of the edges by paths of length m such that every edge is covered exactly two times and every vertex is an end of exactly two paths of the covering. We show that if m :S 2g 3 then: (1) every 2m-regular graph G of girth 9 has an m-PPD, (2) for even m, every m-regular bipartite graph G of girth 9 has a decompositon into paths of length m; moreover such a graph has an m-PPDC.
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ورودعنوان ژورنال:
- Australasian J. Combinatorics
دوره 19 شماره
صفحات -
تاریخ انتشار 1999