From a Zoo to a Zoology: Towards a General Theory of Graph Polynomials

Authors:
J. A. Makowsky
Affiliations:
Technion–Israel Institute of Technology, Department of Computer Science, Haifa, Israel
Venue:
Theory of Computing Systems
Year:
2008

Citing 0
Cited 11

Uniform Algebraic Reducibilities between Parameterized Numeric Graph Invariants

CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Evaluations of Graph Polynomials

Graph-Theoretic Concepts in Computer Science
Connection Matrices for MSOL-Definable Structural Invariants

ICLA '09 Proceedings of the 3rd Indian Conference on Logic and Its Applications
The equivalence of two graph polynomials and a symmetric function

Combinatorics, Probability and Computing
An extension of the bivariate chromatic polynomial

European Journal of Combinatorics
A Most General Edge Elimination Polynomial - Thickening of Edges

Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
Complexity of the Bollobás-Riordan polynomial: exceptional points and uniform reductions

CSR'08 Proceedings of the 3rd international conference on Computer science: theory and applications
The enumeration of vertex induced subgraphs with respect to the number of components

European Journal of Combinatorics
Rapid mixing of subset Glauber dynamics on graphs of bounded tree-width

ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
The complexity of the cover polynomials for planar graphs of bounded degree

MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Almost linear time computation of the chromatic polynomial of a graph of bounded tree-width

LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We outline a general theory of graph polynomials which covers all the examples we found in the vast literature, in particular, the chromatic polynomial, various generalizations of the Tutte polynomial, matching polynomials, interlace polynomials, and the cover polynomial of digraphs. We introduce two classes of (hyper)graph polynomials definable in second order logic, and outline a research program for their classification in terms of definability and complexity considerations, and various notions of reducibilities.