Mark Siggers, The reconfiguration problem for graph homomorpisms

The reconfiguration problem for graph homomorpisms
Mark Siggers
Department of Mathematics, Kyungpook National University, Daegu
2018/04/03 Tue 5PM
For problems with a discrete set of solutions, a reconfiguration problem defines solutions to be adjacent if they meet some condition of closeness, and then asks for two given solutions it there is a path between them in the set of all solutions.
The reconfiguration problem for graph homomorphisms has seen fair activity in recent years. Fixing a template, the problem Recol(H) for a graph H asks if one can get from one H-colouring of a graph G to another by changing one vertex at a time, always remaining an H-colouring. If the changed vertex has a loop, it must move to an adjecent vertex
Depending on H, the problem seems to be either polynomial time solvable or PSPACE-complete. We discuss many recent results in the area and work towards conjecturing for which H the problem is PSPACE-complete.
This is joint work with Rick Brewster, Jae-baek Lee, Ben Moore and Jon Noel.


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