Example
Z2(3) = 7. That is, every seven-edge subgraph of K3,3 contains a 4-cycle K2,2, but there exist 6-edge subgraphs of K3,3 with no 4-cycle. One such 6-edge graph is shown below in Figure A. However, because K3,3 only has nine edges in total, its seven-edge subgraphs are formed by removing exactly two of its edges. If the two removed edges meet at a vertex, as in Figure B, the remaining graph contains three different 4-cycles, one of which is shown in the figure. If the two removed edges do not meet, as in Figure C, the remaining graph contains two 4-cycles, one of which is shown.
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Figure A
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Figure B
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Figure C
Read more about this topic: Zarankiewicz Problem
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