Algorithms for Enumerating All Spanning Trees ofUndirected and Weighted Graphs
SIAM Journal on Computing
Reverse search for enumeration
Discrete Applied Mathematics - Special volume: first international colloquium on graphs and optimization (GOI), 1992
An Optimal Algorithm for Scanning All Spanning Trees of Undirected Graphs
SIAM Journal on Computing
Analytic combinatorics of non-crossing configurations
Discrete Mathematics - Special issue on selected papers in honor of Henry W. Gould
Lower bounds on the number of crossing-free subgraphs of KN
Computational Geometry: Theory and Applications
Sequences of spanning trees and a fixed tree theorem
Computational Geometry: Theory and Applications - Special issue on: Sixteenth European Workshop on Computational Geometry (EUROCG-2000)
Algorithms for Enumerating All Perfect, Maximum and Maximal Matchings in Bipartite Graphs
ISAAC '97 Proceedings of the 8th International Symposium on Algorithms and Computation
An efficient algorithm for enumeration of triangulations
Computational Geometry: Theory and Applications
Enumerating pseudo-triangulations in the plane
Computational Geometry: Theory and Applications
Graphs of Triangulations and Perfect Matchings
Graphs and Combinatorics
Transforming spanning trees and pseudo-triangulations
Information Processing Letters
Counting and Enumerating Pointed Pseudotriangulations with the Greedy Flip Algorithm
SIAM Journal on Computing
A quadratic distance bound on sliding between crossing-free spanning trees
Computational Geometry: Theory and Applications
On the Number of Plane Geometric Graphs
Graphs and Combinatorics
Enumerating Non-crossing Minimally Rigid Frameworks
Graphs and Combinatorics
Gray Code Enumeration of Plane Straight-Line Graphs
Graphs and Combinatorics
Enumerating Constrained Non-crossing Minimally Rigid Frameworks
Discrete & Computational Geometry
A new approach for speeding up enumeration algorithms and its application for matroid bases
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Enumerating constrained non-crossing geometric spanning trees
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Counting plane graphs with exponential speed-up
Rainbow of computer science
Counting crossing-free structures
Proceedings of the twenty-eighth annual symposium on Computational geometry
Counting plane graphs: perfect matchings, spanning cycles, and Kasteleyn's technique
Proceedings of the twenty-eighth annual symposium on Computational geometry
Counting plane graphs: Perfect matchings, spanning cycles, and Kasteleyn's technique
Journal of Combinatorial Theory Series A
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A non-crossing geometric graph is a graph embedded on a given set of points in the plane with non-crossing straight line segments. In this paper we present a new general framework for enumerating non-crossing geometric graphs for a given point set. By applying our idea to specific enumeration problems, we obtain faster algorithms for enumerating plane straight-line graphs, non-crossing spanning connected graphs, non-crossing spanning trees and non-crossing minimally rigid frameworks. Furthermore, we also obtain efficient enumeration algorithms for non-crossing geometric graph classes, for which no enumeration algorithm has been reported so far, such as non-crossing matchings, non-crossing blue-and-red matchings, non-crossing k-vertex or k-edge connected graphs or non-crossing directed spanning trees. The proposed idea is relatively simple, and can be potentially applied to various other enumeration problems of non-crossing geometric graphs.