We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
A proper coloring of the edges of a graph G is called acyclic if there is no 2-colored cycle in G. The acyclic edge chromatic number of G, denoted by a (G), is the least number of...
A 4-graph is odd if its vertex set can be partitioned into two sets so that every edge intersects both parts in an odd number of points. Let b(n) = max n 3 + (n - ) 3 = 1 2 + o...
A graph G with n vertices and maximum degree G cannot be given weak sense of direction using less than G colours. It is known that n colours are always sufficient, and it was conje...
We study a novel clustering problem in which the pairwise relations between objects are categorical. This problem can be viewed as clustering the vertices of a graph whose edges a...
Francesco Bonchi, Aristides Gionis, Francesco Gull...