We show that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. The proof uses an efficient algorithm which a.a.s. 3colours a random 4-regular ...
We give a simple formulation of Karr’s algorithm for computing all affine relationships in affine programs. This simplified algorithm runs in time O(nk3 ) where n is the progr...
We address a question posed by Sibley and Wagon. They proved that rhombic Penrose tilings in the plane can be 3colored, but a key lemma of their proof fails in the natural 3D gene...
: A metric defined by Fine induces a topology on the unit interval which is strictly stronger than the ordinary Euclidean topology and which has some interesting applications in Wa...
This study considers a relaxation of the truck and trailer routing problem (TTRP), called the relaxed truck and trailer routing problem (RTTRP). In the TTRP, the number of availab...