Open Access
February, 1983 A Method of Investigating the Longest Paths in Certain Random Graphs
T. Nemetz, N. Kusolitsch
Ann. Probab. 11(1): 217-221 (February, 1983). DOI: 10.1214/aop/1176993670


In this paper we consider specific directed graphs called "ladders". The vertices of the graph are randomly colored by green or red. Deleting the edges with at least one red endpoint one gets a random graph. We give a method for finding the exact asymptotics of the longest path of this random graph if the "height" of the ladder goes to infinity. The result is a generalization of a celebrated theorem of Erdos-Renyi. An example is given, illustrating the method.


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T. Nemetz. N. Kusolitsch. "A Method of Investigating the Longest Paths in Certain Random Graphs." Ann. Probab. 11 (1) 217 - 221, February, 1983.


Published: February, 1983
First available in Project Euclid: 19 April 2007

zbMATH: 0504.60034
MathSciNet: MR682811
Digital Object Identifier: 10.1214/aop/1176993670

Primary: 60F15
Secondary: 05C20‎ , 60F10

Keywords: Erdos-Renyi laws , large deviation , longest runs , random graph

Rights: Copyright © 1983 Institute of Mathematical Statistics

Vol.11 • No. 1 • February, 1983
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