tinygarden - A java package for testing properties of spanning trees

Abstract Spanning trees are fundamental objects in graph theory. The spanning tree set size of an arbitrary graph can be very large. This limitation discourages its analysis. However interesting patterns can emerge in small cases. In this article we introduce tinygarden, a java package for validating hypothesis, testing properties and discovering patterns from the spanning tree set of an arbitrary graph.

[1]  Eugene W. Myers,et al.  Finding All Spanning Trees of Directed and Undirected Graphs , 1978, SIAM J. Comput..

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Robert E. Tarjan,et al.  Bounds on Backtrack Algorithms for Listing Cycles, Paths, and Spanning Trees , 1975, Networks.

[4]  A. Cayley.  A theorem on trees , 2009 .

[5]  David Eppstein,et al.  Spanning Trees and Spanners , 2000, Handbook of Computational Geometry.

[6]  Fernando Asteasuain,et al.  Una metaheurística GRASP para integración en grafos , 2017 .

[7]  Rui Xu,et al.  Survey of clustering algorithms , 2005, IEEE Transactions on Neural Networks.

[8]  G. Kirchhoff.  Ueber die Auflösung der Gleichungen, auf welche man bei der Untersuchung der linearen Vertheilung galvanischer Ströme geführt wird , 1847 .

[9]  Jason Cong,et al.  Performance optimization of VLSI interconnect layout , 1996, Integr..

[10]  Gabriel Taubin,et al.  Minimum Spanning Tree Cycle Intersection Problem , 2021, Discret. Appl. Math..

[11]  Narsingh Deo,et al.  Algorithms for Generating Fundamental Cycles in a Graph , 1982, TOMS.

[12]  W. T. Tutte,et al.  A Contribution to the Theory of Chromatic Polynomials , 1954, Canadian Journal of Mathematics.

[13]  Kurt Mehlhorn,et al.  Cycle bases in graphs characterization, algorithms, complexity, and applications , 2009, Comput. Sci. Rev..

[14]  Brendan D. McKay,et al.  Practical graph isomorphism, II , 2013, J. Symb. Comput..