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Title: | Evaluating the rank generating function of a graphic 2-polymatroid |
Authors: | Noble, SD |
Keywords: | Polymatroid;Rank generating function;Matroid;Computational complexity;#P-hard;Graph |
Issue Date: | 2006 |
Publisher: | Cambridge University Press |
Citation: | Combinatorics, Probability and Computing 15: 449-461, May 2006 |
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/818 |
DOI: | https://doi.org/10.1017/s0963548305007285 |
ISSN: | 0963-5483 |
Appears in Collections: | Computer Science Mathematical Sciences |
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