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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 and Gelasio SALAZAR. Stars and Bonds in Crossing-Critical Graphs. \textit{Journal of Graph Theory}. New York: John Wiley \&{} Sons, 2010, vol.~65, No~3, p.~198-215. ISSN~0364-9024.
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