International Symposium on Graph Drawing and Network Visualization

Graph Drawing and Network Visualization pp 75-86 | Cite as

On Degree Properties of Crossing-Critical Families of Graphs

  • Drago Bokal
  • Mojca Bračič
  • Marek Derňár
  • Petr Hliněný
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9411)

Abstract

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 \(\min (D)\ge 3\) and \(3,4\in D\), 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.

Keywords

Crossing number Tile drawing Degree-universality Average degree Crossing-critical graph 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Drago Bokal
    • 1
  • Mojca Bračič
    • 1
  • Marek Derňár
    • 2
  • Petr Hliněný
    • 2
  1. 1.Faculty of Natural Sciences and MathematicsUniversity of MariborMariborSlovenia
  2. 2.Faculty of InformaticsMasaryk UniversityBrnoCzech Republic

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