The Onset of Difficulty in A Variant of Graph Coloring and the Jamming Transition

We describe a variant of the well-known graph coloring problem (COL) which we are calling Continuous K-coloring (CONT-COL). This variant has certain properties that make it more amenable to measurement of the computational effort required to find solutions to instances of the problem. We describe the experiments to measure this which we are designing as well. The algorithm used for this purpose is based on the physics algorithm known as the event chain algorithm, which works well with the measures of computational effort we intend to use. These experiments are intended to explore a tentative analogy between the difficulty of various instances of the graph coloring problem and the jamming transition in granular materials from physics, which analogy could add to our understanding of such systems. ∗[email protected] †Funded by NSF REU grant ‡[email protected]