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Abstract: A class of finite structures has a 0--1 law with respect to a logic if every property expressible in the logic has a probability approaching a limit of 0 or 1 as the structure size grows. To formulate 0--1 laws for maps (i.e., embeddings of graphs in a surface), it is necessary to represent maps as logical structures. Three such representations are given, the most general being the full cross representation based on Tutte's theory of combinatorial maps. The main result says that if a class of... (Update)
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BibTeX entry: (Update)
@article{ bender99laws,
author = "Edward A. Bender and Kevin J. Compton and Bruce Richmond",
title = "0-1 laws for maps",
journal = "Random Structures and Algorithms",
volume = "14",
number = "3",
pages = "215-237",
year = "1999",
url = "citeseer.ist.psu.edu/322633.html" }
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2 Submaps of maps III: k-connected nonplanar maps (context) - Bender, Richmond - 1992
2 Random structures and zero-one laws (context) - Winkler - 1993
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