This paper deals with the problem of coloring a two-dimensional segmentation result in such a way that each segment has a different color with the constraint that adjacent segments have sufficiently distinct colors to be easily distinguishable by a human viewer. Our solution for this problem is based on a balanced coloring of the neighborhood graph built from the area Voronoi diagram. The balan...

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5. Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph. For each parameter set, we must decide which strongly regular graphs, if any, possessing the set are 5-chromatic. In this way, we deal completely with 34 of these parameter se...

In order to obtain perfect state transfer between two sites in a network of interacting qubits, their corresponding vertices in the underlying graph must satisfy a property called strong cospectrality. Here we determine the structure of graphs containing pairs of vertices which are strongly cospectral and satisfy a certain extremal property related to the spectrum of the graph. If the graph sat...

Let D be a strongly connected digraph. The strong distance between two vertices u and v in D, denoted by sdD(u; v) is the minimum size of a strongly connected subdigraph of D containing u and v. The strong eccentricity, se(u), of a vertex u of D, is the strong distance between u and a vertex farthest from u. The minimum strong eccentricity among the vertices of D is the strong radius, srad(D), ...

By a game in coalitional structure or shortly coalitional game we mean the standard cooperative non-transferable utility game described by a nonempty set of payo®s for each coalition of players. It is well-known that balancedness is a su±cient condition for the nonemptiness of the core of such a cooperative non-transferable utility game. But any information on the internal organization of the c...

It was only recently shown by Shi and Wormald, using the differential equation method to analyse an appropriate algorithm, that a random 5-regular graph asymptotically almost surely has chromatic number at most 4. Here, we show that the chromatic number of a random 5-regular graph is asymptotically almost surely equal to 3, provided a certain four-variable function has a unique maximum at a giv...