Chromatic symmetric functions and combinatorial polynomials are central constructs in modern algebraic combinatorics, extending classical graph invariants into rich algebraic frameworks. Originating ...

We derive a formula for the chromatic polynomial of a chordal or a triangulated graph in terms of its maximal cliques. As a corollary we obtain a way to write down an explicit formula for the ...

Abstract: This article aims to study the chromatic polynomial of some families of graphs and to describe the properties of the chromatic polynomial of some graph operations. In addition, we will ...

We develop the concept of partition categories, in order to extend the Mullin-Rota theory of binomial enumeration, and simultaneously to provide a natural setting for recent applications of the ...

Abstract: The b-chromatic number of a graph, written as φ(G), is the highest number of colors you can use to color the graph properly, with one special rule: in each color group, there must be at ...

Conjecture 1 (Tutte [2]): If G is a 2-edge-connected graph, then G admits a nowhere-zero 5-flow. If true, Conjecture 1 would imply that for every integer k > 4, the flow polynomial of any ...

In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph — a ...

A research collaboration between the School of Mathematical Sciences at Queen Mary and the Department of Computer Science at Liverpool received recognition at the recent "International Colloquium on ...