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Inequalities of Bonferroni-Galambos Type with Applications to the Tutte Polynomial and the Chromatic Polynomial  
 
  Authors: Klaus Dohmen, Peter Tittmann,  
  Keywords: Bonferroni inequalities, Inclusion-exclusion, Tutte polynomial, Chromatic polynomial, Graph, Matroid  
  Date Received: 16/03/04  
  Date Accepted: 10/06/04  
  Subject Codes:

Primary: 05A20, secondary: 05B35, 05C15,

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

In this paper, we generalize the classical Bonferroni inequalities and their improvements by Galambos to sums of type $ sum_{Isubseteq U} (-1)^{vert Ivert} f(I) $ where $ U$ is a finite set and $ f:2^Urightarrowmathbb{R}$. The result is applied to the Tutte polynomial of a matroid and the chromatic polynomial of a graph. ;


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