A categorification for the chromatic polynomial
نویسندگان
چکیده
منابع مشابه
The Chromatic Polynomial of Fatgraphs and Its Categorification
Motivated by Khovanov homology and relations between the Jones polynomial and graph polynomials, we construct a homology theory for embedded graphs from which the chromatic polynomial can be recovered as the Euler characteristic. For plane graphs, we show that our chromatic homology can be recovered from the Khovanov homology of an associated link. We apply this connection with Khovanov homolog...
متن کاملCategorification of the Dichromatic Polynomial for Graphs
For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate nspecialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs. Also, for each graph and integer n ≤ 2, we define the different one variable n-specializations of the dichromatic polynomials, a...
متن کاملA categorification of the Jones polynomial
2 Preliminaries 5 2.1 The ring R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2 The algebra A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.3 Algebra A and (1+1)-dimensional cobordisms . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Kauffman bracket . . . . . . . . . . . . . . . . . . . ...
متن کاملOn Khovanov’s Categorification of the Jones Polynomial
The working mathematician fears complicated words but loves pictures and diagrams. We thus give a no-fancy-anything picture rich glimpse into Khovanov’s novel construction of “the categorification of the Jones polynomial”. For the same low cost we also provide some computations, including one that shows that Khovanov’s invariant is strictly stronger than the Jones polynomial and including a tab...
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 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: Algebraic & Geometric Topology
سال: 2005
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2005.5.1365