منابع مشابه
Chromatic polynomials of partition systems
The theory of the umbral chromatic polynomial of a simplicial complex provides a combinatorial framework for the study of formal group laws over a commutative, torsion free ring, and our aim in this work is to extend its definition to a class of set systems P, which we label partition systems. When suitably evaluated, our polynomial χ(P; §) enumerates factorized colorings, as well as coloring f...
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 کاملBoundary 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 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 کاملProof of a Chromatic Polynomial Conjecture
In this paper, all graphs considered are simple graphs. We always suppose that G is a graph. Let V(G), E(G), v(G), and e(G) be the vertex set, edge set, order and number of edges of G. For a positive integer *, a *-colouring of G is a mapping f : V(G) [1, ..., *] such that f (x){ f ( y) whenever x and y are adjacent in G. Let P(G, *) denote the number of *-colourings in G. It is well known that...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00125-8