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    Evaluating the rank generating function of a graphic 2-polymatroid

    Noble, Steven (2006) Evaluating the rank generating function of a graphic 2-polymatroid. Combinatorics, Probability and Computing 15 (3), pp. 449-461. ISSN 0963-5483.

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    Abstract

    We consider the complexity of the two-variable rank generating function, $S$, of a graphic 2-polymatroid. For a graph $G$, $S$ is the generating function for the number of subsets of edges of $G$ having a particular size and incident with a particular number of vertices of $G$. We show that for any $x, y \in \mathbb{Q}$ with $xy \not =1$, it is #P-hard to evaluate $S$ at $(x,y)$. We also consider the $k$-thickening of a graph and computing $S$ for the $k$-thickening of a graph.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Sarah Hall
    Date Deposited: 20 Jul 2020 11:46
    Last Modified: 20 Jul 2020 11:46
    URI: https://eprints.bbk.ac.uk/id/eprint/32600

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