Partition of a bipartite hamiltonian graph into two cycles
Discrete Mathematics
Journal of Combinatorial Theory Series B
On the square of a Hamiltonian cycle in dense graphs
Proceedings of the seventh international conference on Random structures and algorithms
Bipartite graphs containing every possible pair of cycles
Discrete Mathematics
2-factors in dense bipartite graphs
Discrete Mathematics - Kleitman and combinatorics: a celebration
Ore-type graph packing problems
Combinatorics, Probability and Computing
On 2-factors of a bipartite graph
Journal of Graph Theory
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Let $G$ and $H$ be balanced $U,V$-bigraphs on $2n$ vertices with $\Delta(H)\leq2$. Let $k$ be the number of components of $H$, $\delta_U:=\min\{\deg_G(u):u\in U\}$ and $\delta_V:=\min\{\deg_G(v):v\in V\}$. We prove that if $n$ is sufficiently large and $\delta_U+\delta_V\geq n+k$, then $G$ contains $H$. This answers a question of Amar in the case that $n$ is large. We also show that $G$ contains $H$ even when $\delta_U+\delta_V\geq n+2$ as long as $n$ is sufficiently large in terms of $k$ and $\delta(G)\geq\frac{n}{200k}+1$.