When you get stuck on a fiendishly difficult sudoku, it’s hard not to wonder if the puzzle really has a solution. At another moment, aglow in the triumph of a clever deduction, you might have a ...

Chemical graph theory provides a rigorous framework for representing molecular structures as graphs, where vertices denote atoms and edges represent bonds. This mathematical abstraction facilitates ...

Commutative algebra and graph theory are two vibrant areas of mathematics that have grown increasingly interrelated. At this interface, algebraic methods are applied to study combinatorial structures, ...

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 ...