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Classification of eight dimensional perfect forms
 MATH
, 2007
"... In this paper, we classify the perfect lattices in dimension 8. There are 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible. ..."
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In this paper, we classify the perfect lattices in dimension 8. There are 10916 of them. Our classification heavily relies on exploiting symmetry in polyhedral computations. Here we describe algorithms making the classification possible.
Engineering an Efficient Canonical Labeling Tool for Large and Sparse Graphs
"... The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate ..."
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Cited by 13 (1 self)
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The problem of canonically labeling a graph is studied. Within the general framework of backtracking algorithms based on individualization and refinement, data structures, subroutines, and pruning heuristics especially for fast handling of large and sparse graphs are developed. Experiments indicate that the algorithm implementation in most cases clearly outperforms existing stateoftheart tools.
Generating irreducible triangulations of surfaces
, 2006
"... Abstract. Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined for the surfaces S0, S1, N1,and N2. An algorithm i ..."
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Cited by 5 (0 self)
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Abstract. Starting with the irreducible triangulations of a fixed surface and splitting vertices, all the triangulations of the surface up to a given number of vertices can be generated. The irreducible triangulations have previously been determined for the surfaces S0, S1, N1,and N2. An algorithm is presented for generating the irreducible triangulations of a fixed surface using triangulations of other surfaces. This algorithm has been implemented as a computer program which terminates for S1, S2, N1, N2, N3, and N4. Thus the complete sets irreducible triangulations are now also known for S2, N3, and N4, with respective cardinalities 396784, 9708, and 6297982. 1.
Polyhedral representation conversion up to symmetries
, 2009
"... We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfu ..."
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Cited by 4 (2 self)
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We give a short survey on computational techniques which can be used to solve the representation conversion problem for polyhedra up to symmetries. In particular we discuss decomposition methods, which reduce the problem to a number of lower dimensional subproblems. These methods have been successfully used by different authors in special contexts. Moreover, we sketch an incremental method, which is a generalization of Fourier–Motzkin elimination, and we give some ideas how symmetry can be exploited using pivots.
Computers and Discovery in Algebraic Graph Theory
 Edinburgh, 2001), Linear Algebra Appl
, 2001
"... We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory. ..."
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Cited by 1 (0 self)
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We survey computers systems which help to obtain and sometimes provide automatically conjectures and refutations in algebraic graph theory.
A Constructive Enumeration of Fusenes and Benzenoids
"... In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using ..."
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Cited by 1 (0 self)
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In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.
A Constructive Enumeration of Fusenes and Benzenoids
"... In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using ..."
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In this paper, a fast and complete method to constructively enumerate fusenes and benzenoids is given. It is fast enough to construct several million non isomorphic structures per second. The central idea is to represent fusenes as labelled inner duals and generate them in a two step approach using the canonical construction path method and the homomorphism principle.
Gunnar Brinkmann
, 2003
"... A graph is chromaticindexcritical if it cannot be edgecoloured with ∆ colours (with ∆ the maximal degree of the graph), and if the removal of any edge decreases its chromatic index. The Critical Graph Conjecture stated that any such graph has odd order. It has been proved false and the smallest k ..."
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A graph is chromaticindexcritical if it cannot be edgecoloured with ∆ colours (with ∆ the maximal degree of the graph), and if the removal of any edge decreases its chromatic index. The Critical Graph Conjecture stated that any such graph has odd order. It has been proved false and the smallest known counterexample has order 18 [18, 31]. In this paper we show that there are no chromaticindexcritical graphs of order 14. Our result extends that of [5] and leaves order 16 as the only case to be checked in order to decide on the minimality of the counterexample given by Chetwynd and Fiol. In addition we list all nontrivial critical graphs of order 13. Key words: critical graph, edgecolouring, graph generation. Math. Subj. Class (2001): 05C15, 05C30