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Interval minors of bipartite graphs were recently introduced by Jacob Fox in the study of Stanley-Wilf limits.
We investigate the maximum number of edges in $K_{r,s}$-interval minor free bipartite graphs.
We determine exact values when $r=2$ and describe the extremal graphs. For $r=3$, lower and upper bounds
are given and the structure of $K_{3,s}$-interval minor free graphs is studied.
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