Incidence matrices Cycles 4 Following problem 4 Graph labeling 4 Graph labelings 4 Incidence matrix 4 Kernel 4 Labeling 4 Labelings 4 Multiplicative version 4 Polynomial algorithm 4 Positive integers 4 Possible solutions 4 Toric ideal 4 Toric ideals 4 Algorithms 2 Alternative approach 2 Bidirected graph 2 Clique cover 2 Combinatorial optimization 2 Constraint Logic Programming 2 Edmonds-Johnson property 2 Graph theory 2 Integer programming 2 Integer solutions 2 Logic programming 2 Perfect graph 2 bidirected graphs 2 claw-free perfect graphs 2 clique cover 2