Thursday, April 21, 2016 — 2:30 PM EDT

Ross Willard, Department of Pure Mathematics, University of Waterloo

“Bipartite graphs with interesting polymorphisms”

Given a finite graph G, the Retract Problem Ret(G) is conjectured to be solvable in polynomial time if and only if, for some n > 1, there exists a retraction r of Gn onto the “diagonal subgraph ∆n(G) = {(v, v, . . . , v) : v V (G)} of Gn which moreover satisfies r(v1,v2,...,vn) = r(v2,...,vn,v1). A retract of this kind is called an n-ary cyclic poly- morphism of G. More generally, a retract of Gn onto ∆n(G) is called an n-ary idempotent polymorphism of G, and there are many open problems regarding the structure of graphs admitting an idempotent polymorphism with specified properties. In this lecture I will survey what is known and state some open problems.

MC 5479

**Please Note Room**

S M T W T F S
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
31
1
2
3
4
  1. 2022 (60)
    1. May (12)
    2. April (14)
    3. March (15)
    4. February (12)
    5. January (7)
  2. 2021 (135)
    1. December (11)
    2. November (22)
    3. October (15)
    4. September (5)
    5. August (15)
    6. July (17)
    7. June (15)
    8. May (1)
    9. April (4)
    10. March (11)
    11. February (9)
    12. January (10)
  3. 2020 (103)
  4. 2019 (199)
  5. 2018 (212)
  6. 2017 (281)
  7. 2016 (335)
  8. 2015 (211)
  9. 2014 (235)
  10. 2013 (251)
  11. 2012 (135)