Arcs in graphs are NOT pairs of nodes

Let H be a class of given graphs. A graph G is said to be H-free if G contains no induced copies of H for every H?H. A graph is called traceable if it contains a Hamilton path. Faudree and Gould (1997) characterized all the pairs {R,S} of connected ...

For an integer k with k>=2 and a pair of connected graphs F"1 and F"2 of order at least three, we say that {F"1,F"2} is a k-forbidden pair if every k-connected {F"1,F"2}-free graph, except possibly for a finite number of exceptions, is Hamiltonian. If ...

Two graphs are said to be chromatically equivalent if they have the same chromatic polynomial. In this paper we give the means to construct infinitely many pairs of chromatically equivalent graphs where one graph in the pair is clique-separable, that is,...