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Bounded maximum degree conjecture holds precisely for c-crossing-critical graphs with c<=12

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F19%3A10401459" target="_blank" >RIV/00216208:11320/19:10401459 - isvavai.cz</a>

  • Result on the web

    <a href="https://doi.org/10.4230/LIPIcs.SoCG.2019.14" target="_blank" >https://doi.org/10.4230/LIPIcs.SoCG.2019.14</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.4230/LIPIcs.SoCG.2019.14" target="_blank" >10.4230/LIPIcs.SoCG.2019.14</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Bounded maximum degree conjecture holds precisely for c-crossing-critical graphs with c<=12

  • Original language description

    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 &gt;= 13 and d &gt;= 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 &lt;=12, precisely, that there exists a constant D such that every c-crossing-critical graph with c &lt;=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 Dvorák and Mohar (without an explicit construction), holds true, surprisingly, exactly for the values c &lt;=12.

  • Czech name

  • Czech description

Classification

  • Type

    D - Article in proceedings

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GA17-04611S" target="_blank" >GA17-04611S: Ramsey-like aspects of graph coloring</a><br>

  • Continuities

    P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Others

  • Publication year

    2019

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Article name in the collection

    35th International Symposium on Computational Geometry (SoCG 2019)

  • ISBN

    978-3-95977-104-7

  • ISSN

    1868-8969

  • e-ISSN

  • Number of pages

    15

  • Pages from-to

    1-15

  • Publisher name

    Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik

  • Place of publication

    Dagstuhl, Germany

  • Event location

    Portland, Oregon

  • Event date

    Jun 18, 2019

  • Type of event by nationality

    WRD - Celosvětová akce

  • UT code for WoS article