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

Transactions of the American Mathematical Society, Vol. 332, No. 2 (Aug., 1992), pp. 729-756 (28 pages) In this paper we present several results and open problems about log-concavity properties of ...

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 ...

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 ...

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 ...