Graphs & digraphs (2nd ed.)
An extension of the multi-path algorithm for finding Hamilton cycles
Discrete Mathematics - Special volume (part two) to mark the centennial of Julius Petersen's “Die theorie der regula¨ren graphs” (“The theory of regular graphs”)
Polynomial Algorithms for Hamiltonian Cycle in Cocomparability Graphs
SIAM Journal on Computing
On some properties of DNA graphs
Discrete Applied Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Graphs and Hypergraphs
Linear-time algorithms for the Hamiltonian problems on distance-hereditary graphs
Theoretical Computer Science
A polynomial algorithm for the Hamiltonian cycle problem in semicomplete multipartite digraphs
Journal of Graph Theory
Finding Hamiltonian circuits in quasi-adjoint graphs
Discrete Applied Mathematics
Computational complexity of isothermic DNA sequencing by hybridization
Discrete Applied Mathematics - Special issue: IV ALIO/EURO workshop on applied combinatorial optimization
On a simple randomized algorithm for finding a 2-factor in sparse graphs
Information Processing Letters
Complexity Issues in Computational Biology
Fundamenta Informaticae - Watching the Daisies Grow: from Biology to Biomathematics and Bioinformatics — Alan Turing Centenary Special Issue
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The results presented in the paper are threefold. Firstly, a new class of reduced-by-matching directed graphs is defined and its properties studied. The graphs are output from the algorithm which, for a given 1-graph, removes arcs which are unnecessary from the point of view of searching for a Hamiltonian circuit. In the best case, the graph is reduced to a quasi-adjoint graph, what results in polynomial-time solution of the Hamiltonian circuit problem. Secondly, the systematization of several classes of digraphs, known from the literature and referring to directed line graphs, is provided together with the proof of its correctness. Finally, computational experiments are presented in order to verify the effectiveness of the reduction algorithm.