منابع مشابه
Boundary chromatic polynomial
We consider proper colorings of planar graphs embedded in the annulus, such that vertices on one rim can take Qs colors, while all remaining vertices can take Q colors. The corresponding chromatic polynomial is related to the partition function of a boundary loop model. Using results for the latter, the phase diagram of the coloring problem (with real Q and Qs) is inferred, in the limits of two...
متن کاملApproximating the Chromatic Polynomial
Chromatic polynomials are important objects in graph theory and statistical physics, but as a result of computational difficulties, their study is limited to graphs that are small, highly structured, or very sparse. We have devised and implemented two algorithms that approximate the coefficients of the chromatic polynomial P (G,x), where P (G, k) is the number of proper k-colorings of a graph G...
متن کاملThe Chromatic Polynomial
It is shown how to compute the Chromatic Polynomial of a simple graph utilizing bond lattices and the Möbius Inversion Theorem, which requires the establishment of a refinement ordering on the bond lattice and an exploration of the Incidence Algebra on a partially ordered set.
متن کاملOn Chromatic Polynomial and Ordinomial
1 1 Introduction 2 1 Introduction Suppose Γ is a graph with |V (Γ)| = n. For λ a positive integer, let [λ] = {1, 2,. .. , λ} be a set of λ distinct colors. A λ-coloring of Γ is a mapping f from V (Γ) to [λ]. Whenever for every two adjacent vertices u and v, f (u) = f (v), we will call f a proper coloring of Γ; otherwise, improper. When a proper λ-coloring exists, we call Γ a λ-colorable graph. ...
متن کاملCategorifications of the chromatic polynomial
We will discuss different categorifications of the chromatic polynomial, how they are related to each other as well as how they relate to the Hochschild homology of algebras and Khovanov link homology.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2008
ISSN: 0022-4715,1572-9613
DOI: 10.1007/s10955-008-9585-0