THIS SITE

Information for

Graphs and Matroids Seminar - Bruce RichterExport this event to calendar

Thursday, November 16, 2017 — 3:30 PM EST

Title: Convex drawings of complete graphs:  topology meets geometry

Speaker: Bruce Richter
Affiliation: University of Waterloo
Room: MC 5479

Abstract:

A drawing D of the complete graph K(n) is the sphere is characterized by, for each isomorph J of K(5), D[J] is homeomorphic to one of the three rectilinear drawings of K(5).  Every drawing of K(n) in the plane with all edges straight-line segments is obviously convex.  Thus, convex drawings generalize planar point sets that are in general position. Some geometric properties of planar point sets carry over to convex drawings:  there are O(n2) “empty triangles” and, for each r, if n is large enough, every convex drawing of K(n) contains a “natural K(r)”. However, our interest is centred on trying to prove that every drawing of K(n) with a minimum number of crossings must be convex.  In this talk, I will describe a theorem that is a first step in this direction.

Location 
MC - Mathematics & Computer Building
5479
200 University Avenue West
Waterloo, ON N2L 3G1
Canada

S M T W T F S
29
30
31
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
1
2
  1. 2017 (96)
    1. November (16)
    2. October (11)
    3. September (7)
    4. August (3)
    5. July (5)
    6. June (9)
    7. May (10)
    8. April (7)
    9. March (13)
    10. February (10)
    11. January (5)
  2. 2016 (137)
    1. December (5)
    2. November (12)
    3. October (10)
    4. September (8)
    5. August (12)
    6. July (15)
    7. June (14)
    8. May (16)
    9. April (8)
    10. March (18)
    11. February (11)
    12. January (8)
  3. 2015 (136)
  4. 2014 (88)
  5. 2013 (48)
  6. 2012 (39)
  7. 2011 (36)
  8. 2010 (40)
  9. 2009 (40)
  10. 2008 (39)
  11. 2007 (15)