A note on the conditional chromatic polynomial
نویسندگان
چکیده
منابع مشابه
A Note on Chromatic Sum
The chromatic sum Σ(G) of a graph G is the smallest sum of colors among of proper coloring with the natural number. In this paper, we introduce a necessary condition for the existence of graph homomorphisms. Also, we present Σ(G) < χf (G)|G| for every graph G.
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1. Definitions and a main result 2 1.1. Graphs and colorings . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2. Symmetric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3. Chromatic symmetric functions . . . . . . . . . . . . . . . . . . . . . 5 1.4. Connected components . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.5. Circuits and broken circuits . . . . ...
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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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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.
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1994
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500030834