The study of graph colouring has long been a central topic in discrete mathematics, with a prominent focus on optimising the assignment of labels or colours to vertices such that adjacent vertices are ...

Abstract. In the present paper we are interested in the study of the distance Laplacian eigenvalues of a connected graph with fixed order n and chromatic number χ. We prove lower bounds on the ...

This paper proves that for any integer n ≥ 4 and any rational number r, 2 ≤ r ≤ n — 2, there exists a graph G which has circular chromatic number r and which does not contain Kn as a minor. Journal ...

Let G be a graph and k a natural number. A k-coloring of G is a map c that maps the vertices of G into the set {1, 2, ..., k} (whose elements are called colors) such that no two adjacent vertices are ...