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@inproceedings{1309625,
author = {Bokal, Drago and Bračič, Mojca and Derňár, Marek and Hliněný, Petr},
address = {Berlin},
booktitle = {Graph Drawing and Network Visualization 2015, Lecture Notes in Computer Science 9411},
doi = {http://dx.doi.org/10.1007/978-3-319-27261-0_7},
edition = {LNCS 9411},
editor = {Emilio Di Giacomo, Anna Lubiw},
keywords = {Crossing number; Tile drawing; Degree-universality; Average degree; Crossing-critical graph},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Berlin},
isbn = {978-3-319-27260-3},
pages = {75-86},
publisher = {Springer Verlag},
title = {On Degree Properties of Crossing-critical Families of Graphs},
year = {2015}
}
TY - JOUR
ID - 1309625
AU - Bokal, Drago - Bračič, Mojca - Derňár, Marek - Hliněný, Petr
PY - 2015
TI - On Degree Properties of Crossing-critical Families of Graphs
PB - Springer Verlag
CY - Berlin
SN - 9783319272603
KW - Crossing number
KW - Tile drawing
KW - Degree-universality
KW - Average degree
KW - Crossing-critical graph
N2 - Answering an open question from 2007, we construct infinite k-crossing-critical families of graphs which contain vertices of any prescribed odd degree, for sufficiently large k. From this we derive that, for any set of integers D such that min(D)>=3 and 3,4eD, and for all sufficiently large k there exists a k-crossing-critical family such that the numbers in D are precisely the vertex degrees which occur arbitrarily often in any large enough graph in this family. We also investigate what are the possible average degrees of such crossing-critical families.
ER -
BOKAL, Drago, Mojca BRAČIČ, Marek DERŇÁR and Petr HLINĚNÝ. On Degree Properties of Crossing-critical Families of Graphs. In Emilio Di Giacomo, Anna Lubiw. \textit{Graph Drawing and Network Visualization 2015, Lecture Notes in Computer Science 9411}. LNCS 9411. Berlin: Springer Verlag, 2015, p.~75-86. ISBN~978-3-319-27260-3. Available from: https://dx.doi.org/10.1007/978-3-319-27261-0\_{}7.
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