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SUMMARY:Meghana M. Reddy (ETH Zürich)
DTSTART:20230309T151500Z
DTEND:20230309T170000Z
DTSTAMP:20260422T065705Z
UID:CJCS/105
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CJCS/105/">O
 n the Number of Edges in Maximal 2-planar Graphs</a>\nby Meghana M. Reddy 
 (ETH Zürich) as part of Copenhagen-Jerusalem Combinatorics Seminar\n\n\nA
 bstract\nA graph is 2-planar if it has local crossing number two\, that is
 \, it can be drawn in the plane such that every edge has at most two cross
 ings. A graph is maximal 2-planar if no edge can be added such that the re
 sulting graph remains 2-planar. A 2-planar graph on n vertices has at most
  5n-10 edges\, and some (maximal) 2-planar graphs---referred to as optimal
  2-planar---achieve this bound. However\, in strong contrast to maximal pl
 anar graphs\, a maximal 2-planar graph may have fewer than the maximum pos
 sible number of edges. In this paper\, we determine the minimum edge densi
 ty of maximal 2-planar graphs by proving that every maximal 2-planar graph
  on n vertices has at least 2n edges. We also show that this bound is tigh
 t\, up to an additive constant. The lower bound is based on an analysis of
  the degree distribution in specific classes of drawings of the graph. The
  upper bound construction is verified by carefully exploring the space of 
 admissible drawings using computer support. This is joint work with Michae
 l Hoffmann.\n
LOCATION:https://researchseminars.org/talk/CJCS/105/
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