. . . . . "Stars and Bonds in Crossing-Critical Graphs"@en . "Stars and Bonds in Crossing-Critical Graphs"@en . "Salazar, Gelasio" . . . "2"^^ . "1571-0653" . . "Hlin\u011Bn\u00FD, Petr" . "14330" . "The structure of all known infinite families of crossing--critical graphs has led to the conjecture that crossing--critical graphs have bounded bandwidth. If true, this would imply that crossing--critical graphs have bounded degree, that is, that they cannot contain subdivisions of $K_{1,n}$ for arbitrarily large $n$. In this paper we prove two results that revolve around this conjecture. On the positive side, we show that crossing--critical graphs cannot contain subdivisions of $K_{2,n}$ for arbitrarily large $n$. On the negative side, we show that there are graphs with arbitrarily large maximum degree that are $2$-crossing--critical in the projective plane." . "31" . "RIV/00216224:14330/08:00024776" . "RIV/00216224:14330/08:00024776!RIV10-GA0-14330___" . "[360E633C6981]" . . . "Electronic Notes in Discrete Mathematics" . "397227" . "1" . "5"^^ . "Stars and Bonds in Crossing-Critical Graphs" . . . "crossing number; crossing-critical graph"@en . "The structure of all known infinite families of crossing--critical graphs has led to the conjecture that crossing--critical graphs have bounded bandwidth. If true, this would imply that crossing--critical graphs have bounded degree, that is, that they cannot contain subdivisions of $K_{1,n}$ for arbitrarily large $n$. In this paper we prove two results that revolve around this conjecture. On the positive side, we show that crossing--critical graphs cannot contain subdivisions of $K_{2,n}$ for arbitrarily large $n$. On the negative side, we show that there are graphs with arbitrarily large maximum degree that are $2$-crossing--critical in the projective plane."@en . "1"^^ . . "Stars and Bonds in Crossing-Critical Graphs" . "FR - Francouzsk\u00E1 republika" . . "P(GA201/08/0308)" .