Edge-Colored Graph Theory is a vibrant area within combinatorics that extends the classical study of graphs by assigning colours to edges. This paradigm not only uncovers subtle structural ...

Nov. 20, 2019 Te size-Ramsey number of a path presented by Louis DeBiasio, Ph.D., Miami University Abstract: Given a graph H, the size-Ramsey number of H is the minimum m such that there exists a ...

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks — vertices (dots) and edges (lines connecting them) — has been an invaluable way ...

But assessing for planarity amid the addition and removal of edges is difficult without drawing the graph yourself and trying not to cross any lines (See “The Three Utilities Problem” below ...

In their 2019 paper Holm and Rotenberg found that some drawings provide a more advantageous starting position for inserting an edge than others. These “good” drawings are only a few flips away from ...

Edge-Colored Graph Theory is a vibrant area within combinatorics that extends the classical study of graphs by assigning colours to edges.

Graph theory isn’t enough. The mathematical language for talking about connections, which usually depends on networks—vertices (dots) and edges (lines connecting them)—has been an invaluable ...