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

Graph colouring is a fundamental problem in both theoretical and applied combinatorics, with significant implications for computer science, operational research and network theory. At its essence, ...

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 ...

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 a recent article, mathematicians explain the use of tools from the branch of mathematics called graph theory to systematically analyze Sudoku puzzles. They also find that analyzing Sudokus leads to ...

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 ...