The Amazing Chromatic Polynomial
نویسندگان
چکیده
منابع مشابه
Approximating 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...
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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...
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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. ...
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ژورنال
عنوان ژورنال: The Mathematical Intelligencer
سال: 2022
ISSN: ['0343-6993', '1866-7414']
DOI: https://doi.org/10.1007/s00283-021-10136-z