Let G = (V, E) be a graph. Let c : V → N be a vertex-coloring of the vertices of G. For any vertex u, we denote by N[u] its closed neighborhood (u and its adjacent vertices), an...
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
Attempts to solve the famous Four Color Problem led to fruitful discoveries and rich coloring theories. In this talk, some old and some recent applications of tools from topology ...
We establish that every cyclically 4-connected cubic planar graph of order at most 40 is hamiltonian. Furthermore, this bound is determined to be sharp and we present all nonhamil...
Robert E. L. Aldred, S. Bau, Derek A. Holton, Bren...