"P(GA201/08/0308)" . "Hv\u011Bzdy a \u0159ezy v pr\u016Fse\u010D\u00EDkov\u011B kritick\u00FDch grafech"@cs . "[E43AFB9045A9]" . . "1571-0653" . . "5"^^ . "RIV/00216224:14330/08:00024776!RIV09-GA0-14330___" . "Stars and Bonds in Crossing-Critical Graphs"@en . "Elsevier" . "Prezentujeme dva p\u0159\u00EDstupy k dosud otev\u0159en\u00E9 domn\u011Bnce, \u017Ee pr\u016Fse\u010D\u00EDkov\u011B kritick\u00E9 grafy maj\u00ED omezen\u00FD maxim\u00E1ln\u00ED stupe\u0148. Na pozitivn\u00ED stran\u011B dokazujeme, \u017Ee tyto grafy nemohou obsahovat subdivizi velk\u00E9ho K_2,n, ale na negativn\u00ED stran\u011B ukazujeme neplatnost domn\u011Bnky v projektivn\u00ED rovin\u011B."@cs . "1"^^ . . "Paris, France" . "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." . . . "2"^^ . . "Stars and Bonds in Crossing-Critical Graphs" . "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 . "Stars and Bonds in Crossing-Critical Graphs" . . "14330" . "397228" . . "crossing number; crossing-critical graph"@en . . "The International Conference on Topological and Geometric Graph Theory TGGT2008, Electronic Notes in Discrete Mathematics 31, 2008" . . "RIV/00216224:14330/08:00024776" . . "2008-05-19+02:00"^^ . . "Hlin\u011Bn\u00FD, Petr" . . "Stars and Bonds in Crossing-Critical Graphs"@en . "Salazar, Gelasio" . "Hv\u011Bzdy a \u0159ezy v pr\u016Fse\u010D\u00EDkov\u011B kritick\u00FDch grafech"@cs . . . "Nizozemi" .