A generalization of Tutte's characterization of totally unimodular matrices
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
String and graph reduction systems for gene assembly in ciliates
Mathematical Structures in Computer Science
Computation in Living Cells: Gene Assembly in Ciliates (Natural Computing Series)
Computation in Living Cells: Gene Assembly in Ciliates (Natural Computing Series)
Journal of Combinatorial Theory Series B
Parallel complexity of signed graphs for gene assembly in ciliates
Soft Computing - A Fusion of Foundations, Methodologies and Applications
Graph theoretic approach to parallel gene assembly
Discrete Applied Mathematics
The parallel complexity of signed graphs: Decidability results and an improved algorithm
Theoretical Computer Science
DNA'04 Proceedings of the 10th international conference on DNA computing
Pivots, determinants, and perfect matchings of graphs
Theoretical Computer Science
Pivots, determinants, and perfect matchings of graphs
Theoretical Computer Science
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We describe a graph reduction operation, generalizing three graph reduction operations related to gene assembly in ciliates. The graph formalization of gene assembly considers three reduction rules, called the positive rule, double rule, and negative rule, each of which removes one or two vertices from a graph. The graph reductions we define consist precisely of all compositions of these rules. We study graph reductions in terms of the adjacency matrix of a graph over the finite field F"2, and show that they are path invariant, in the sense that the result of a sequence of graph reductions depends only on the vertices removed. The binary rank of a graph is the rank of its adjacency matrix over F"2. We show that the binary rank of a graph determines how many times the negative rule is applied in any sequence of positive, double, and negative rules reducing the graph to the empty graph, resolving two open problems posed by Harju, Li, and Petre. We also demonstrate the close relationship between graph reductions and the matrix pivot operation, both of which can be studied in terms of the poset of subsets of vertices of a graph that can be removed by a graph reduction.