The pre-coloring extension problem consists, given a graph G and a set of nodes to which some colors are already assigned, in finding a coloring of G with the minimum number of co...
The structural properties of graphs are usually characterized in terms of invariants, which are functions of graphs that do not depend on the labeling of the nodes. In this paper ...
Venkat Chandrasekaran, Pablo A. Parrilo, Alan S. W...
We present a short way of proving the inequalities obtained by Wright in [Journal of Graph Theory, 4: 393 – 407 (1980)] concerning the number of connected graphs with ℓ edges m...
We show how to use split decomposition to compute the weighted clique number and the chromatic number of a graph and we apply these results to some classes of graphs. In particular...
It has long been known that the number of spanning trees in circulant graphs with fixed jumps and n nodes satisfies a recurrence relation in n. The proof of this fact was algebra...