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We address the enumeration of properly q-colored planar maps, or more precisely, the enumeration of rooted planar maps M weighted by their chromatic polynomial \chi_M(q) and counted by the number of vertices and faces.
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Dichromatic sums for rooted planar maps
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On the random cluster model: I. Introduction and relation to other models
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Chromatic sums for rooted planar triangulations. II. The case λ = τ + 1 \lambda=\tau+1
W. T. Tutte · 1973
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Chromatic sums for rooted planar triangulations. III. The case λ = 3 \lambda=3
W. T. Tutte · 1973
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Chromatic sums for rooted planar triangulations. IV. The case λ = ∞ \lambda=\infty
W. T. Tutte · 1973
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Chromatic sums for rooted planar triangulations: the cases λ = 1 \lambda=1 and λ = 2 \lambda=2
W. T. Tutte · 1973
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Chromatic sums for rooted planar triangulations. V. Special equations
W. T. Tutte · 1974
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On a pair of functional equations of combinatorial interest
W. T. Tutte · 1978
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Limits of chromatic zeros of some families of maps
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Chromatic solutions. II
W. T. Tutte · 1982
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Combinatorial enumeration
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On the interpretation of Whitney numbers through arrangements of hyperplanes, zonotopes, non-Radon partitions, and orientations of graphs
C. Greene and T. Zaslavsky · 1983
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A differential equation arising in chromatic sum theory
A. M. Odlyzko and L. B. Richmond · 1983
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Chromatic sum equations for rooted planar maps
Y. Liu · 1984
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Map-colourings and differential equations
W. T. Tutte · 1984
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The Ising model on a random planar lattice: the structure of the phase transition and the exact critical exponents
D. V. Boulatov and V. A. Kazakov · 1987
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Analytic models and ambiguity of context-free languages
P. Flajolet · 1987
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The Potts model and the Beraha numbers
P. P. Martin · 1987
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On chromatic and dichromatic sum equations
Y. Liu · 1990
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Zeroes of chromatic polynomials: a new approach to Beraha conjecture using quantum groups
H. Saleur · 1990
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Orientations acycliques et le polynôme chromatique
B. Lass · 2001
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Basic analytic combinatorics of directed lattice paths
C. Banderier and P. Flajolet · 2002
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Four classes of pattern-avoiding permutations under one roof: generating trees with two labels
M. Bousquet-Mélou · 2002
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Census of planar maps: from the one-matrix model solution to a combinatorial proof
J. Bouttier, P. Di Francesco, and E. Guitter · 2002
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The degree distribution of bipartite planar maps: applications to the Ising model
M. Bousquet-Mélou and G. Schaeffer · 2003
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The number of degree-restricted rooted maps on the sphere
E. A. Bender and E. R. Canfield · 1994
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Gfun: a Maple package for the manipulation of generating and holonomic functions in one variable
B. Salvy and P. Zimmermann · 1994
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Exact solution of the O ( n ) {O}(n) model on a random lattice
B. Eynard and C. Kristjansen · 1995
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W. T. Tutte · 1995
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B. Eynard and C. Kristjansen · 1996
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Planar maps as labeled mobiles
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Planar maps and algebraic series: a generalization of the quadratic method
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Complex-temperature phase diagram of Potts and RSOS models
J. L. Jacobsen, J.-F. Richard, and J. Salas · 2006
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Bijective counting of tree-rooted maps and shuffles of parenthesis systems
O. Bernardi · 2007
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Dissections and trees, with applications to optimal mesh encoding and to random sampling
É. Fusy, D. Poulalhon, and G. Schaeffer · 2008
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Asymptotic enumeration of constellations and related families of maps on orientable surfaces
G. Chapuy · 2009
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