We prove that for every tree T of order at least 2 and every minimum dominating set D of T which contains at most one endvertex of T, there is an independent dominating set I of T...
A dominating set D of a graph G = (V, E) is a subset of vertices such that every vertex in V \ D has at least one neighbour in D. Moreover if D is an independent set, i.e. no verti...
We present the first polynomial-time approximation scheme (PTAS) for the Minimum Independent Dominating Set problem in graphs of polynomially bounded growth. Graphs of bounded gr...
A graph is uniquely hamiltonian if it contains exactly one hamiltonian cycle. In this note we prove that there are no r-regular uniquely hamiltonian graphs when r > 22. This im...
Penny E. Haxell, Ben Seamone, Jacques Verstraë...