Chip firing and divisorial graph gonality

Series: 
Graph Theory Seminar
Thursday, January 19, 2017 - 15:05
1 hour (actually 50 minutes)
Location: 
Skiles 005
,  
TU Delft
,  
Organizer: 
Consider the following solitaire game on a graph. Given a chip configuration on the node set V, a move consists of taking a subset U of nodes and sending one chip from U to V\U along each edge of the cut determined by U. A starting configuration is winning if for every node there exists a sequence of moves that allows us to place at least one chip on that node. The (divisorial) gonality of a graph is defined as the minimum number of chips in a winning configuration. This notion belongs to the Baker-Norine divisor theory on graphs and can be seen as a combinatorial analog of gonality for algebraic curves. In this talk we will show that the gonality is lower bounded by the tree-width and, if time permits, that the parameter is NP-hard to compute. We will conclude with some open problems.