Results 1 to 10 of about 2,394 (219)
A new two-variable generalization of the chromatic polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2003 We present a two-variable polynomial, which simultaneously generalizes the chromatic polynomial, the independence polynomial, and the matching polynomial of a graph.
Klaus Dohmen +2 more
doaj +3 more sources
A categorification of the chromatic symmetric polynomial [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Stanley chromatic polynomial of a graph $G$ is a symmetric function generalization of the chromatic polynomial, and has interesting combinatorial properties.
Radmila Sazdanović, Martha Yip
doaj +3 more sources
More connections between the matching polynomial and the chromatic polynomial
AKCE International Journal of Graphs and Combinatorics, 2019 The connection between the matching polynomial and the chromatic polynomial for triangle-free graphs was revealed in the work of Farrell and Whitehead. We extend this result to all graph by mirroring the corresponding result of Godsil and Gutman for the ...
Beatriz Carely Luna-Olivera +2 more
doaj +4 more sources
Algorithms for computing chromatic polynomials and chromatic index polynomials
Scientific AfricanObjectives: The aim of this article is to enhance the understanding of the computation of chromatic polynomials and chromatic index polynomials, and to facilitate their practical use in various fields by demonstrating and supporting the proposed ...
Lateram Zawuga Hordofa +2 more
doaj +2 more sources
Chromatic Polynomials of Mixed Hypercycles
Discussiones Mathematicae Graph Theory, 2014 We color the vertices of each of the edges of a C-hypergraph (or cohypergraph) in such a way that at least two vertices receive the same color and in every proper coloring of a B-hypergraph (or bihypergraph), we forbid the cases when the vertices of any ...
Allagan Julian A., Slutzky David
doaj +2 more sources
Bears with Hats and Independence Polynomials [PDF]
Discrete Mathematics & Theoretical Computer Science, 2023 Consider the following hat guessing game. A bear sits on each vertex of a graph $G$, and a demon puts on each bear a hat colored by one of $h$ colors. Each bear sees only the hat colors of his neighbors.
Václav Blažej +2 more
doaj +1 more source
Chromatic Schultz and Gutman Polynomials of Jahangir Graphs J2,m and J3,m
Journal of Applied Mathematics, 2023 Topological polynomial and indices based on the distance between the vertices of a connected graph are widely used in the chemistry to establish relation between the structure and the properties of molecules.
Ramy Shaheen +2 more
doaj +1 more source
Connection between Graphs' Chromatic and Ehrhart Polynomials [PDF]
Journal of Applied Sciences and Nanotechnology, 2023 Graph Theory is a discipline of mathematics with numerous outstanding issues and applications in a variety of sectors of mathematics and science. The chromatic polynomial is a type of polynomial that has useful and attractive qualities.
Ola Neamah, Shatha Salman
doaj +1 more source
Problems on chromatic polynomials of hypergraphs
Electronic Journal of Graph Theory and Applications, 2020 Chromatic polynomials of graphs have been studied extensively for around one century. The concept of chromatic polynomial of a hypergraph is a natural extension of chromatic polynomial of a graph. It also has been studied for more than 30 years.
Ruixue Zhang, Fengming Dong
doaj +1 more source
Burnside Chromatic Polynomials of Group-Invariant Graphs
Discussiones Mathematicae Graph Theory, 2023 We introduce the Burnside chromatic polynomial of a graph that is invariant under a group action. This is a generalization of the Q-chromatic function Zaslavsky introduced for gain graphs.
White Jacob A.
doaj +1 more source