Graphical condensation for enumerating perfect matchings
نویسندگان
چکیده
منابع مشابه
Graphical condensation for enumerating perfect matchings
The method of graphical condensation for enumerating perfect matchings was found by Propp (Theoretical Computer Science 303(2003), 267-301), and was generalized by Kuo (Theoretical Computer Science 319 (2004), 29-57). In this paper, we obtain some more general results on graphical condensation than Kuo’s. Our method is also different from Kuo’s. As applications of our results, we obtain a new p...
متن کاملApplications of graphical condensation for enumerating matchings and tilings
A technique called graphical condensation is used to prove various combinatorial identities among numbers of (perfect) matchings of planar bipartite graphs and tilings of regions. Graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph, and then re-partitioning the united matching (actually a multigraph) into matchings of two other subgraphs, in o...
متن کاملA Fast Algorithm for Enumerating Bipartite Perfect Matchings
In this paper, we propose an algorithm for enumerating all the perfect matchings included in a given bipartite graph G = (V,E). The algorithm is improved by the approach which we proposed at ISAAC98. Our algorithm takes O(log |V |) time per perfect matching while the current fastest algorithm takes O(|V |) time per perfect matching. Keyword: enumeration, enumerating algorithm, perfect matching.
متن کاملGraphical condensation of plane graphs: A combinatorial approach
The method of graphical vertex-condensation for enumerating perfect matchings of plane bipartite graph was found by Propp (Theoret. Comput. Sci. 303(2003), 267-301), and was generalized by Kuo (Theoret. Comput. Sci. 319 (2004), 29-57) and Yan and Zhang (J. Combin. Theory Ser. A, 110(2005), 113125). In this paper, by a purely combinatorial method some explicit identities on graphical vertex-cond...
متن کاملGraphical Condensation, Overlapping Pfaffians and Superpositions of Matchings
The purpose of this note is to exhibit clearly how the “graphical condensation” identities of Kuo, Yan, Yeh and Zhang follow from classical Pfaffian identities by the Kasteleyn–Percus method for the enumeration of matchings. Knuth termed the relevant identities “overlapping Pfaffian” identities and the key concept of proof “superpositions of matchings”. In our uniform presentation of the materi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2005
ISSN: 0097-3165
DOI: 10.1016/j.jcta.2004.10.005