Geodesic
Ovoids and Bipartite Subgraphs in Generalized Quadrangles
Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 878-885.

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A point-line incidence system is called an $\alpha$-partial geometry of order $(s,t)$ if each line contains $s + 1$ points, each point lies on $t + 1$ lines, and for any point $a$ not lying on a line $L$, there exist precisely $\alpha$ lines passing through $a$ and intersecting $L$ (the notation is $pG_\alpha(s,t)$). If $\alpha = 1$, then such a geometry is called a generalized quadrangle and denoted by $GQ(s,t)$. It is established that if a pseudogeometric graph for a generalized quadrangle $GQ(s,s^2-s)$ contains more than two ovoids, then $s = 2$. It is proved that the point graph of a generalized quadrangle GQ(4,t) contains no K 4,6-subgraphs. Finally, it is shown that if some $\mu$-subgraph of a pseudogeometric graph for a generalized quadrangle $GQ(4,t)$ contains a triangle, then $t\le6$. 
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     title = {Ovoids and {Bipartite} {Subgraphs} in {Generalized} {Quadrangles}},
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A. A. Makhnev (Jr.); A. A. Makhnev. Ovoids and Bipartite Subgraphs in Generalized Quadrangles. Matematičeskie zametki, Tome 73 (2003) no. 6, pp. 878-885. http://geodesic.mathdoc.fr/item/MZM_2003_73_6_a8/

[1] Brauver A. E., van Lint I. Kh., “Silno regulyarnye grafy i chastichnye geometrii”, Kiberneticheskii sbornik, 24 (1987), 186–229

[2] Paine S., Thas J., Finite generalized quadrangles, Pitman, Boston, 1985

[3] Haemers W., “There exists no $(76,21,2,7)$ strongly regular graph”, Finite Geometries and Combinatorics, London Math. Soc. Lecture Notes, 191, eds. F. De Clerck et. al., Cambridge Univ. Press, Cambridge, 1993, 175–176 | MR | Zbl

[4] Makhnev A. A., “O psevdogeometricheskikh grafakh nekotorykh chastichnykh geometrii”, Voprosy algebry, no. 11, Izd-vo Gomelskogo universiteta, Gomel, 1997, 60–67 | MR

[5] Wilbrink H. A., Brouwer A. E., “$(57,14,1)$ strongly regular graph does not exist”, Proc. Kon. Nederl. Akad. Ser. A, 45:1 (1983), 117–121 | MR | Zbl