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A Graph Polynomial for Independent Sets of Bipartite Graphs

Published online by Cambridge University Press:  10 July 2012

Q. GE  and
D. ŠTEFANKOVIČ
Q. GE
Affiliation:
Department of Computer Science, University of Rochester, Rochester, NY 14627–0226, USA (e-mail: qge@cs.rochester.edu and stefanko@cs.rochester.edu)
D. ŠTEFANKOVIČ
Affiliation:
Department of Computer Science, University of Rochester, Rochester, NY 14627–0226, USA (e-mail: qge@cs.rochester.edu and stefanko@cs.rochester.edu)
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Abstract

We introduce a new graph polynomial that encodes interesting properties of graphs, for example, the number of matchings, the number of perfect matchings, and, for bipartite graphs, the number of independent sets (#BIS).

We analyse the complexity of exact evaluation of the polynomial at rational points and show a dichotomy result: for most points exact evaluation is #P-hard (assuming the generalized Riemann hypothesis) and for the rest of the points exact evaluation is trivial.

Keywords

Primary 05C31Secondary 03D15
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 21 , Issue 5 , September 2012 , pp. 695 - 714
Copyright
Copyright © Cambridge University Press 2012

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