Geodesic
Maximum size of a planar graph ($\Delta=3$, $D=3$)
Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 159-171

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The problem of maximum size of a graph of diameter 3 and maximum degree 3 as a function of its Euler characteristics is studied. The negative solution of an Erdös problem is obtained. A new approach to such problems is proposed which consists in counting the paths between different pairs of vertices in a graph. 
@article{FPM_2001_7_1_a9,
     author = {S. A. Tishchenko},
     title = {Maximum size of a planar graph ($\Delta=3$, $D=3$)},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {159--171},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a9/}
}
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S. A. Tishchenko. Maximum size of a planar graph ($\Delta=3$, $D=3$). Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 1, pp. 159-171. http://geodesic.mathdoc.fr/item/FPM_2001_7_1_a9/