The Degree Sequence of Random Graphs from Subcritical Classes

NICLA BERNASCONI, KONSTANTINOS PANAGIOTOU, ANGELIKA STEGER
2009 Combinatorics, probability & computing  
In this work we determine the expected number of vertices of degree k = k(n) in a graph with n vertices that is drawn uniformly at random from a subcritical graph class. Examples of such classes are outerplanar, series-parallel, cactus and clique graphs. Moreover, we provide exponentially small bounds for the probability that the quantities in question deviate from their expected values. † Parts of this work appeared as an extended abstract in N. Bernasconi, K. Panagiotou and A. Steger, 'On the
more » ... degree sequences of random outerplanar and series-parallel graphs ', in APPROX-RANDOM 2008 , pp. 303-316.
doi:10.1017/s0963548309990368 fatcat:liahgjzflbh5tmxk5t4bjxtppa