2 problems

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Connectivity conjecture for the triangle-pseudoline incidence graph
Triangle-pseudoline incidence graph conjecture. The triangle-pseudoline incidence graph of a pseudoline arrangement is connected.
Conjectureopencombinatorial-geometry incidence-graphs pseudoline-arrangementsarXiv posted 2 days ago
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The nonexistence conjecture for M-property incidence graphs of 2-quasi-symmetric designs
Nonexistence conjecture. There are no point-line incidence graphs of a $2$ -quasi-symmetric design with $x=0$ that have the $M$ -property.
Conjectureopendesign-theory distance-regular-graphs incidence-graphsarXiv posted 2 days ago

Connectivity conjecture for the triangle-pseudoline incidence graph