Paper Info
Title
Fixed Points and 2-Cycles of Synchronous Dynamic Coloring Processes on Trees.
Abstract
This paper considers synchronous discrete-time dynamical systems on graphs based on the threshold model. It is well known that after a finite number of rounds these systems either reach a fixed point or enter a 2-cycle. The problem of finding the fixed points for this type of dynamical system is in general both NP-hard and #P-complete. In this paper we give a surprisingly simple graph-theoretic characterization of fixed points and 2-cycles for the class of finite trees. Thus, the class of trees is the first nontrivial graph class for which a complete characterization of fixed points exists. This characterization enables us to provide bounds for the total number of fixed points and pure 2-cycles. It also leads to an output-sensitive algorithm to efficiently generate these states.
Year
DOI
Venue
2022
10.1007/978-3-031-09993-9_15
Colloquium on Structural Information & Communication Complexity (SIROCCO)
DocType
Citations 
PageRank 
Conference
0
0.34
References 
Authors
0
1
Name
Order
Citations
PageRank
Volker Turau1122.17