If true, the following conjecture of Thomassen [Th81] is a planarity criterion for a special class of graphs that involves only K 5. Recall that a planar graph on n vertices contains at most 3n-6 ...

Graph partitioning and bisection problems occupy a central position in combinatorial optimisation and theoretical computer science. These issues involve dividing a graph’s vertex set into distinct ...

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 ...

Graph reconfiguration and colouring problems investigate the transition between feasible solutions of a graph colouring instance. The central challenge is to determine a series of elementary vertex ...

The legendary graph isomorphism problem may be harder than a 2015 result seemed to suggest. “In Laci Babai, you have one of the most legendary and fearsome theoretical computer scientists there ever ...

In this video series I show you how to graph linear inequalities. When graphing linear inequalities we now have to account ...