For most of us, the word graph brings back memories (not always pleasant) of pencils and rulers and quadrille ruled paper, though a more recent generation may think instead of pie and bar charts ...

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 core, this ...

Graph homomorphisms and chromatic numbers are foundational concepts in modern graph theory, with widespread applications that extend from combinatorial optimisation to theoretical computer science. A ...