Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
The complexity of harmonious colouring for trees
Discrete Applied Mathematics - Special issue: Combinatorial Optimization 1992 (CO92)
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
The interlace polynomial of a graph
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Some new evaluations of the Tutte polynomial
Journal of Combinatorial Theory Series B
Parity, eulerian subgraphs and the Tutte polynomial
Journal of Combinatorial Theory Series B
From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials
Theory of Computing Systems
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Algorithmic lower bounds for problems parameterized by clique-width
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Intractability of Clique-Width Parameterizations
SIAM Journal on Computing
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A graph polynomial $p(G, \bar{X})$ can code numeric information about the underlying graph G in various ways: as its degree, as one of its specific coefficients or as evaluations at specific points $\bar{X}= \bar{x}_0$. In this paper we study the question how to prove that a given graph parameter, say *** (G ), the size of the maximal clique of G , cannot be a fixed coefficient or the evaluation at any point of the Tutte polynomial, the interlace polynomial, or any graph polynomial of some infinite family of graph polynomials. Our result is very general. We give a sufficient condition in terms of the connection matrix of graph parameter f (G ) which implies that it cannot be the evaluation of any graph polynomial which is invariantly definable in CMSOL , the Monadic Second Order Logic augmented with modular counting quantifiers. This criterion covers most of the graph polynomials known from the literature.