Complete bipartite factorisations of Kn,n
نویسندگان
چکیده
منابع مشابه
A Family of Perfect Factorisations of Complete Bipartite Graphs
A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n=p for an odd prime p. We construct a family of (p−1)/2 non-isomorphic perfect 1-factorisations of Kn, n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltonian if the permutation defined by any row relative to any other row is a single cy...
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Suppose p < q are odd and relatively prime. In this paper we complete the proof that Kn,n has a factorisation into factors F whose components are copies of Kp,q if and only if n is a multiple of pq(p+q). The final step is to solve the “c-value problem” of Martin. This is accomplished by proving the following fact and some variants: For any 0 ≤ k ≤ n, there exists a sequence (π1, π2, . . . , π2k...
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A homogeneous factorisation of a graph is a partition of its arc set such that there exist vertex transitive subgroups M < G 6 Aut(Γ) with M fixing each part of the partition setwise and G preserving the partition and transitively permuting the parts. In this paper we study homogeneous factorisations of complete multipartite graphs such that M acts regularly on vertices. We provide a necessary ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00819-1