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Bounded degree conjecture holds precisely for ▫$c$▫-crossing-critical graphs with ▫$c \leq 12$▫ [Elektronski vir]Bokal, Drago, 1978- ...We study ▫$c$▫-crossing-critical graphs, which are the minimal graphs that require at least ▫$c$▫ edge-crossings when drawn in the plane. For every fixed pair of integers with ▫$c\ge 13$▫ and ▫$d\ge ... 1$▫, we give first explicit constructions of ▫$c$▫-crossing-critical graphs containing a vertex of degree greater than ▫$d$▫. We also show that such unbounded degree constructions do not exist for ▫$c\le 12$▫, precisely, that there exists a constant ▫$D$▫ such that every ▫$c$▫-crossing-critical graph with ▫$c\le 12$▫ has maximum degree at most ▫$D$▫. Hence, the bounded maximum degree conjecture of ▫$c$▫-crossing-critical graphs, which was generally disproved in 2010 by Dvořák and Mohar (without an explicit construction), holds true, surprisingly, exactly for the values ▫$c\le 12$▫.Source: 35th International Symposium on Computational Geometry [Elektronski vir] : SoCG 2019, June 18-21, 2019, Portland, Oregon, USA (15 str.)Type of material - conference contributionPublish date - 2019Language - englishCOBISS.SI-ID - 18858585
Author
Bokal, Drago, 1978- |
Dvořák, Zdeněk |
Hliněný, Petr |
Leanõs, Jesús |
Mohar, Bojan, 1956- |
Wiedera, Tilo
Topics
graph drawing |
crossing number |
crossing-critical |
zip product
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Database name | Field | Year |
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Links to authors' personal bibliographies | Links to information on researchers in the SICRIS system |
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Bokal, Drago, 1978- | 22402 |
Dvořák, Zdeněk | ![]() |
Hliněný, Petr | ![]() |
Leanõs, Jesús | ![]() |
Mohar, Bojan, 1956- | 01931 |
Wiedera, Tilo | ![]() |
Source: Personal bibliographies
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