How to list all possible maximal bipartite matchings in R?

Question

I have an incidence matrix:

Q = matrix(c(0,1,1,1,0,1,1,0,1,0,1,1,1,1,1,0,0,0,0,0,0,0,0,0,0), nrow = 5, ncol=5)
rownames(Q) = c(64,32,47,42,58)
colnames(Q) = c(49,64,88,31,13)

I would like to list all possible max bipartite matchings. Using igraph:

G <- graph_from_incidence_matrix(Q)
M <- max_bipartite_match(G)
M$matching

which gives only one possible maximal matching:

  64   32   47   42   58   49   64   88   31   13 
"64" "49" "88"   NA   NA "32" "64" "47"   NA   NA 

For instance, another one would be:

  64   32   47   42   58   49   64   88   31   13 
"64" "49"   NA   NA   88 "32" "64" "58"   NA   NA 

Is there a way of getting the complete list of all possible bipartite matchings in R?

I have also tried with lpSolve:

res <- lp.assign(Q, "max")

but it also only gives me one possible solution instead of all.

Thanks for your help!