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@article{907768, author = {Hliněný, Petr and Salazar, Gelasio}, article_location = {New York}, article_number = {3}, keywords = {crossing number; crossing-critical graph}, language = {eng}, issn = {0364-9024}, journal = {Journal of Graph Theory}, title = {Stars and Bonds in Crossing-Critical Graphs}, url = {http://dx.doi.org/10.1002/jgt.20473}, volume = {65}, year = {2010} }
TY - JOUR ID - 907768 AU - Hliněný, Petr - Salazar, Gelasio PY - 2010 TI - Stars and Bonds in Crossing-Critical Graphs JF - Journal of Graph Theory VL - 65 IS - 3 SP - 198-215 EP - 198-215 PB - John Wiley & Sons SN - 03649024 KW - crossing number KW - crossing-critical graph UR - http://dx.doi.org/10.1002/jgt.20473 N2 - 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. ER -
HLINĚNÝ, Petr a Gelasio SALAZAR. Stars and Bonds in Crossing-Critical Graphs. \textit{Journal of Graph Theory}. New York: John Wiley \&{} Sons, 2010, roč.~65, č.~3, s.~198-215. ISSN~0364-9024.
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