We examine powers of Hamiltonian paths and cycles as well as Hamiltonian (power) completion problems in several highly structured graph classes. For threshold graphs we give effic...
Gioan showed that the number of cycle reversing classes of totally cyclic orientations of a given graph can be calculated as an evaluation of the corresponding Tutte polynomial. We...
Beifang Chen, Arthur L. B. Yang, Terence Y. J. Zha...
We consider edge-coloured complete graphs. A path or cycle Q is called properly coloured (PC) if any two adjacent edges of Q differ in colour. Our note is inspired by the followi...
The circumference of a graph is the length of its longest cycles. Results of Jackson, and Jackson and Wormald, imply that the circumference of a 3-connected cubic n-vertex graph i...
Pinchasi and Radoiˇci´c [11] used the following observation to bound the number of edges of a topological graph without a self-crossing cycle of length 4: if we make a list of t...