Chromatic polynomial information

The chromatic polynomial is a graph polynomial studied in algebraic graph theory, a branch of mathematics. It counts the number of graph colorings as a...

David Birkhoff introduced the chromatic polynomial to study the coloring problem, which was generalised to the Tutte polynomial by W. T. Tutte, both of which...

The Tutte polynomial, also called the dichromate or the Tutte–Whitney polynomial, is a graph polynomial. It is a polynomial in two variables which plays...

challenging graph isomorphism problem. However, even polynomial-valued invariants such as the chromatic polynomial are not usually complete. The claw graph and...

of graphs, and especially the chromatic polynomial, the Tutte polynomial and knot invariants. The chromatic polynomial of a graph, for example, counts...

graphs. The chromatic polynomial of the bull graph is ( x − 2 ) ( x − 1 ) 3 x {\displaystyle (x-2)(x-1)^{3}x} . Two other graphs are chromatically equivalent...

graph as the chromatic number, denoted by χ(G). The number of proper k-colorings is a polynomial function of k called the chromatic polynomial of our graph...

by that element. The chromatic polynomial of a graph counts the number of proper colourings of that graph. The term "polynomial", as an adjective, can...

Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. The chromatic polynomial, a polynomial whose values...

isomorphic matroids have the same polynomial. The characteristic polynomial of M – sometimes called the chromatic polynomial, although it does not count colorings...

number of q colors, called its chromatic polynomial, remains unknown so far. The scaling of zeros of the chromatic polynomial of random graphs with parameters...

originally introduced by Richard Stanley as a generalization of the chromatic polynomial of a graph. For a finite graph G = ( V , E ) {\displaystyle G=(V...

the chromatic polynomial and Ehrhart polynomial (see below), all special cases of Stanley's general Reciprocity Theorem. The chromatic polynomial P (...

graph that is a unit distance graph in the Euclidean plane. The chromatic polynomial of the wheel graph Wn is : P W n ( x ) = x ( ( x − 2 ) ( n − 1 )...

friendship graph has chromatic number 3 and chromatic index 2n. Its chromatic polynomial can be deduced from the chromatic polynomial of the cycle graph...

the vertices in the reverse of a perfect elimination ordering. The chromatic polynomial of a chordal graph is easy to compute. Find a perfect elimination...

has book thickness 3 and queue number 2. The Pappus graph has a chromatic polynomial equal to: ( x − 1 ) x ( x 16 − 26 x 15 + 325 x 14 − 2600 x 13 + 14950...

2000 spanning trees, the most of any 10-vertex cubic graph. has chromatic polynomial t ( t − 1 ) ( t − 2 ) ( t 7 − 12 t 6 + 67 t 5 − 230 t 4 + 529 t 3...

remains of interest to find examples and only very few are known. The chromatic polynomial of the Brinkmann graph is x21 - 42x20 + 861x19 - 11480x18 + 111881x17...

Acyclic orientations are also related to colorings through the chromatic polynomial, which counts both acyclic orientations and colorings. The planar...

problem, Birkhoff introduced the chromatic polynomial. Even though this line of attack did not prove fruitful, the polynomial itself became an important object...

Visibility graph Museum guard problem Wheel graph Acyclic coloring Chromatic polynomial Cocoloring Complete coloring Edge coloring Exact coloring Four color...

number of acyclic orientations is equal to |χ(−1)|, where χ is the chromatic polynomial of the given graph. Any directed graph may be made into a DAG by...

also a 2-vertex-connected graph and a 2-edge-connected graph. Its chromatic polynomial is ( x − 2 ) ( x − 1 ) x . {\displaystyle (x-2)(x-1)x.} Triangle-free...

June (2012). "Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs". Journal of the American Mathematical Society. 25 (3):...

and quantum field theory. This includes work on the chromatic polynomial and the Tutte polynomial, which appear both in algebraic graph theory and in...