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{\bf Jill R. Faudree,  Ronald J. Gould, Florian Pfender and Allison Wolf }
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{\bf On $k$-Ordered Bipartite Graphs}
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In 1997, Ng and Schultz introduced the idea of cycle orderability. For a positive integer
$k$,  a graph $G$ is {\it k-ordered} if for every ordered sequence of $k$ vertices, there is a cycle
that encounters the vertices of the sequence in the given order.  If the cycle is also a hamiltonian
cycle, then $G$ is said to be {\it k-ordered hamiltonian.} We give minimum degree conditions and
sum of degree conditions for nonadjacent vertices that imply
a balanced bipartite graph to be $k$-ordered hamiltonian. For example, let $G$ be a balanced 
bipartite graph on $2n$ vertices, $n$ sufficiently large. 
We show that for any positive integer $k$,  if the minimum degree of $G$ is at
least $(2n+k-1)/4$, then $G$ is $k$-ordered hamiltonian.

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