Constructs eulerian tours on a graph.

etour-- Constructs an eulerian tour on a graph using Hierholzer's algorithm. Returns a vector of node labels. If weighted is TRUE constructs a weight-decreasing eulerian using the modified Hierholzer's algorithm. Usually etour is not called directly, rather the generic function eulerian is used.

Usage

etour(g, start=NULL,weighted=TRUE)

Arguments

g: a graph satisfying is_even_graph
start: an optional starting node for the tour.
weighted: whether tour uses weights

Details

The supplied graph should satisfyis_even_graph. If weighted is TRUE the lowest weight edge is found, and the tour starts at the one of its nodes, picking the node with the bigger second-smallest edge weight. After that the tour follows weight-increasing edges. If weighted is FALSE weights are ignored. The returned tour is typically a closed path. However, if the last edge is a duplicated edge added to make the graph even, this edge is omitted and the result is an open path.

References

see overview

Author

C.B. Hurley and R.W. Oldford

Examples

require(PairViz)

g <- mk_even_graph(5)

etour(g)
#>  [1] "1" "2" "3" "1" "4" "2" "5" "3" "4" "5" "1"
g <- mk_even_graph(6) # adds 3 extra edges to g, so all nodes are even
etour(g)
#>  [1] "1" "2" "3" "1" "4" "2" "3" "4" "5" "1" "6" "2" "5" "3" "6" "4" "5" "6"
etour(g, start= "4") # modifies the starting node
#>  [1] "4" "1" "2" "3" "1" "5" "2" "3" "4" "2" "6" "1" "6" "3" "5" "4" "6" "5"

eulerian(6) # The eulerian wrapper looks after making even graph,
#>  [1] 1 2 3 1 4 2 3 4 5 1 6 2 5 3 6 4 5 6
#also returns numbers rather than nodes

# On a general graph.
v <- LETTERS[1:4]
g <- new("graphNEL",nodes=v)
g <- addEdge(v[1],v[3:4],g,1:2)
g <- addEdge(v[2],v[3:4],g,3:4)
etour(g) 
#> [1] "C" "A" "D" "B" "C"

eulerian(g) # Equivalently, use eulerian wrapper 
#> [1] "C" "A" "D" "B" "C"


n <- LETTERS[1:5]
g <- new("graphNEL",nodes=n)
g <- addEdge(n[1],n[2:3],g)
g <-addEdge(n[2],n[3:5],g)
g <-addEdge(n[4],n[3],g)
is_even_graph(g)
#> [1] FALSE
etour(mk_even_graph(g))
#> [1] "B" "A" "C" "B" "D" "C" "E" "B"

eulerian(g) # Equivalently, use eulerian wrapper 
#> [1] "B" "A" "C" "B" "D" "C" "E" "B"