E. A. Bender, P. J. Cameron, A. M. Odlyzko, B. L. Richmond  Home/Search
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Abstract: This paper begins with the observation that half of all graphs containing no induced path of length 3 are disconnected. We generalize this in several directions. First, we give necessary and sufficient conditions (in terms of generating functions) for the probability of connectedness in a suitable class of graphs to tend to a limit strictly between zero and one. Next we give a general framework in which this and related questions can be posed, involving operations on classes of finite... (Update)
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BibTeX entry: (Update)
@misc{ bender-connectedness,
author = "E. A. Bender and P. J. Cameron and A. M. Odlyzko and B. L. Richmond",
title = "Connectedness, Classes, and Cycle Index",
url = "citeseer.ist.psu.edu/17097.html" }
Citations (may not include all citations):151 Singularity analysis of generating function (context) - Flajolet, Odlyzko - 1990
80 Free Lie Algebras (context) - Reutenauer - 1994
65 Asymptotic enumeration methods - Odlyzko - 1995
61 the foundations of combinatorial theory (context) - Rota - 1964
51 Une th'eorie combinatoire des s'eries formelles (context) - Joyal - 1981
26 Oligomorphic Permutation Groups (context) - Cameron - 1990
19 Asymmetric graphs (context) - Erdos, R'enyi - 1963
18 Kombinatorische Anzahlbestimmungen fur Gruppen (context) - P'olya - 1937
18 The number of trees (context) - Otter - 1948
16 Universal graphs and universal functions (context) - Rado - 1964
13 A generalisation of Stirling's formula (context) - Hayman - 1956
11 A natural ring basis for the shuffle algebra and an applicat.. (context) - Radford - 1979
6 Sur certains relations qui g'en'eralisent l'ordre des nombre.. (context) - Fraiss'e - 1953
5 the probability of connectedness (context) - Cameron
5 Some remarks on the theory of trees (context) - R'enyi - 1959
3 Enumeration of posets generated by disjoint unions and ordin.. (context) - Stanley - 1974
1 Enumeration of ordered sets (context) - El-Zahar - 1989
1 The algebra of an age - Cameron
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