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
Transforming cabbage into turnip: polynomial algorithm for sorting signed permutations by reversals
Journal of the ACM (JACM)
Formal systems for gene assembly in ciliates
Theoretical Computer Science
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)
The interlace polynomial of a graph
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Journal of Combinatorial Theory Series B
Natural Computing: an international journal
Edge local complementation and equivalence of binary linear codes
Designs, Codes and Cryptography
Graph reductions, binary rank, and pivots in gene assembly
Discrete Applied Mathematics
The group structure of pivot and loop complementation on graphs and set systems
European Journal of Combinatorics
Maximal pivots on graphs with an application to gene assembly
Discrete Applied Mathematics
Graph reductions, binary rank, and pivots in gene assembly
Discrete Applied Mathematics
The group structure of pivot and loop complementation on graphs and set systems
European Journal of Combinatorics
Binary Symmetric Matrix Inversion Through Local Complementation
Fundamenta Informaticae - Words, Graphs, Automata, and Languages; Special Issue Honoring the 60th Birthday of Professor Tero Harju
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We consider sequences of local and edge complementations on graphs with loops (we allow local complementation only on looped vertices). We recall that these operations together form the matrix operation of principal pivot transform (or pivot) restricted to graphs. This fact is not well known, and as a consequence various special cases of the properties of pivot have been rediscovered multiple times. In this paper we give a gentle overview of various properties of pivot for local and edge complementations on graphs. Moreover, we relate the pivot operation to perfect matchings to obtain a purely graph-theoretical characterization of the effect of sequences of pivot operations. Finally, we show that two of the three operations that make up a formal graph model of the biological process of gene assembly in ciliates together form the matrix operation of Schur complement restricted to graphs.