2011/09/19 by Allison Henrich, Henrich, Allison, Inga Johnson +1
Mathematics · #57M15 #91A46 #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT) #math.CO #math.GT #msc:57M15 #msc:91A46
paper · pdf · doi:10.48550/arxiv.1109.4103
Final journal version to appear in AKCE Journal of Graphs and Combinatorics, 15 pages, 13 figures
arxiv created 2012/08/14 · arxiv updated 2012/08/15
We introduce a topological combinatorial game called the Link Smoothing Game. The game is played on the shadow of a link diagram and legal moves consist of smoothing precrossings. One player's goal is to keep the diagram connected while the other player's goal is to disconnect the shadow. We make significant progress towards a complete classification of link shadows into outcome classes by capitalizing on the relationship between link shadows and the planar graphs associated to their checkerboard colorings.