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@article{1600841,
author = {Hliněný, Petr and Korbela, Michal},
article_number = {3},
keywords = {graph; crossing number; crossing-critical},
language = {eng},
issn = {0231-6986},
journal = {Acta Math. Univ. Comenianae},
title = {On the achievable average degrees in 2-crossing-critical graphs},
url = {http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1178/725},
volume = {88},
year = {2019}
}
TY - JOUR
ID - 1600841
AU - Hliněný, Petr - Korbela, Michal
PY - 2019
TI - On the achievable average degrees in 2-crossing-critical graphs
JF - Acta Math. Univ. Comenianae
VL - 88
IS - 3
SP - 787-793
EP - 787-793
SN - 02316986
KW - graph
KW - crossing number
KW - crossing-critical
UR - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1178/725
L2 - http://www.iam.fmph.uniba.sk/amuc/ojs/index.php/amuc/article/view/1178/725
N2 - c-Crossing-critical graphs are the minimal graphs requiring at least c edge crossings in every drawing in the plane. The structure of these obstructions is very rich for every c>=2. Although, at least in the first nontrivial case of c=2, their structure is well understood. For example, we know that, aside of finitely many small exceptions, the 2-crossing-critical graphs have vertex degrees from the set {3, 4, 5, 6} and their average degree can achieve exactly all rational values from the interval [3+1/2 , 4+2/3]. Continuing in depth in this research direction, we determine which average degrees of 2-crossing-critical graphs are possible if we restrict their vertex degrees to proper subsets of {3, 4, 5, 6}. In particular, we identify the (surprising) subcases in which, by number-theoretical reasons, the achievable average degrees form discontinuous sets of rationals.
ER -
HLINĚNÝ, Petr a Michal KORBELA. On the achievable average degrees in 2-crossing-critical graphs. \textit{Acta Math. Univ. Comenianae}. 2019, roč.~88, č.~3, s.~787-793. ISSN~0231-6986.
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