"New infinite families of almost-planar crossing-critical graphs" . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . . . . "12"^^ . "crossing-critical; graph"@en . . . "New infinite families of almost-planar crossing-critical graphs"@en . "1" . . "Hlin\u011Bn\u00FD, Petr" . . "New infinite families of almost-planar crossing-critical graphs"@en . "New infinite families of almost-planar crossing-critical graphs" . . . "Electronic Journal of Combinatorics" . "We show that, for all choices of integers $k>2$ and $m$, there are simple $3$-connected $k$-crossing-critical graphs containing more than $m$ vertices of each even degree $\\leq2k-2$. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least $7$ in crossing-critical graphs remains open. Furthermore, our newly constructed graphs have several other interesting properties; for instance, they are almost planar and their average degree can attain any rational value in the interval $\\big[3+\\frac15,6-\\frac8{k+1}\\big)$."@en . . "[33141A40BB9A]" . "1"^^ . . "000258122700003" . . "1"^^ . "We show that, for all choices of integers $k>2$ and $m$, there are simple $3$-connected $k$-crossing-critical graphs containing more than $m$ vertices of each even degree $\\leq2k-2$. This construction answers one half of a question raised by Bokal, while the other half asking analogously about vertices of odd degrees at least $7$ in crossing-critical graphs remains open. Furthermore, our newly constructed graphs have several other interesting properties; for instance, they are almost planar and their average degree can attain any rational value in the interval $\\big[3+\\frac15,6-\\frac8{k+1}\\big)$." . "382567" . . . "P(1M0545), P(GA201/08/0308), S" . "14330" . "RIV/00216224:14330/08:00025241" . "15" . "RIV/00216224:14330/08:00025241!RIV10-GA0-14330___" . "1077-8926" .