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  Volume 5, Issue 3, Article 64
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,  

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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