### On star polynomials, graphical partitions and reconstruction.

Farrell, E.J., de Matas, C.M. (1988)

International Journal of Mathematics and Mathematical Sciences

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Farrell, E.J., de Matas, C.M. (1988)

International Journal of Mathematics and Mathematical Sciences

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Kuperberg, Greg (2002)

The Electronic Journal of Combinatorics [electronic only]

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Kuperberg, Greg (1998)

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Pretzel, Oliver, Siemons, Johannes (2005)

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F. Y. Wu, C. King, W. T. Lu (1999)

Annales de l'institut Fourier

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The Tutte polynomial is a generalization of the chromatic polynomial of graph colorings. Here we present an extension called the rooted Tutte polynomial, which is defined on a graph where one or more vertices are colored with prescribed colors. We establish a number of results pertaining to the rooted Tutte polynomial, including a duality relation in the case that all roots reside around a single face of a planar graph.

Fayers, Matthew (2008)

The Electronic Journal of Combinatorics [electronic only]

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Carme Àlvarez, Maria Serna (2009)

RAIRO - Theoretical Informatics and Applications

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This paper studies the computational complexity of the problem (), when the input graph is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the and a graph layout problem the (). We show a dichotomy: the and the are NP-complete for colored caterpillars of hair length 2, while both problems are in P for colored caterpillars of hair length 2. For the hardness results we provide a reduction from the , while the...

Berg, Chris, Vazirani, Monica (2008)

The Electronic Journal of Combinatorics [electronic only]

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King, R.C., Welsh, T.A. (2007)

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Eisenkölbl, Theresia (2005)

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