The complexity of searching a graph
Journal of the ACM (JACM)
European Journal of Combinatorics
Chip-Firing Games on Mutating Graphs
SIAM Journal on Discrete Mathematics
Open problems of Paul Erd&ohuml;s in graph theory
Journal of Graph Theory
Classes of lattices induced by chip firing (and sandpile) dynamics
European Journal of Combinatorics
Path decompositions and Gallai's conjecture
Journal of Combinatorial Theory Series B
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Clean the graph before you draw it!
Information Processing Letters
Parallel cleaning of a network with brushes
Discrete Applied Mathematics
Cleaning random d-regular graphs with brushes using a degree-greedy algorithm
CAAN'07 Proceedings of the 4th conference on Combinatorial and algorithmic aspects of networking
Fast edge-searching and related problems
COCOA'10 Proceedings of the 4th international conference on Combinatorial optimization and applications - Volume Part II
Fast edge searching and fast searching on graphs
Theoretical Computer Science
Fast searching games on graphs
Journal of Combinatorial Optimization
POLISH-Let us play the cleaning game
Theoretical Computer Science
Hi-index | 5.23 |
Following the decontamination metaphor for searching a graph, we introduce a cleaning process, which is related to both the chip-firing game and edge searching. Brushes (instead of chips) are placed on some vertices and, initially, all the edges are dirty. When a vertex is 'fired', each dirty incident edge is traversed by only one brush, cleaning it, but a brush is not allowed to traverse an already cleaned edge; consequently, a vertex may not need degree-many brushes to fire. The model presented is one where the edges are continually recontaminated, say by algae, so that cleaning is regarded as an on-going process. Ideally, the final configuration of the brushes, after all the edges have been cleaned, should be a viable starting configuration to clean the graph again. We show that this is possible with the least number of brushes if the vertices are fired sequentially but not if fired in parallel. We also present bounds for the least number of brushes required to clean graphs in general and some specific families of graphs.