Graph polynomials serve as robust algebraic encodings of the intricate combinatorial properties inherent to graphs. At the heart of this discipline lies the Tutte polynomial, an invariant that not ...

Abstract. Let 𝐼(𝐺;𝑥) denote the independence polynomial of a graph 𝐺. In this paper we study the unimodality properties of 𝐼(𝐺;𝑥) for some composite graphs 𝐺. Given two graphs 𝐺₁ and 𝐺₂, let ...

Daniel Lokshtanov’s work explores the limits of what computers can solve, paving the way for advances in artificial intelligence and computational efficiency.

In [1], the following result is proved: Theorem: Let k be a positive integer and let G be a 3-connected infinite planar graph of subexponential growth. Then G contains infinitely many disjoint k-paths ...

In an isomorphic copy of the ring of symmetric polynomials we study some families of polynomials which are indexed by rational weight vectors. These families include well known symmetric polynomials, ...