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 ...

The Erdős–Pósa property forms a pivotal concept in modern graph theory by establishing a profound duality between the problems of packing and covering cycles or other substructures. At its ...

The main challenge here lies in devising a mathematically acceptable proof of this impossibility, which is where the foundations for what we today know as graph theory.

Mathematicians have proved that copies of smaller graphs can always be used to perfectly cover larger ones. On January 8, three mathematicians posted a proof of a nearly 60-year-old problem in ...