Binomial edge ideals constitute a vibrant research area where the methods of commutative algebra intersect with the combinatorial structures inherent in graph theory. By associating to each graph an ...

The 2-domination number γ₂(G) of a graph G is the minimum cardinality of a set S ⊆ V(G) such that every vertex from V(G) \ S is adjacent to at least two vertices in S. The annihilation number a(G) is ...

In 1950 Edward Nelson, then a student at the University of Chicago, asked the kind of deceptively simple question that can give mathematicians fits for decades. Imagine, he said, a graph — a ...

Imagine 100 dots scattered in front of you. In a haphazard variation on connect-the-dots, start drawing lines between the points. How many lines can you draw without producing a triangle? A square? An ...