In this paper we study the performance of a particular on-line coloring algorithm, the First-Fit or Greedy algorithm, on a class of perfect graphs namely the permutation graphs. W...
Let X be the random variable that counts the number of triangles in the binomial random graph G(n, p). We show that for some positive constant c, the probability that X deviates f...
For an integer k > 0, a graph G is k-triangular if every edge of G lies in at least k distinct 3-cycles of G. In (J Graph Theory 11:399–407 (1987)), Broersma and Veldman propo...
A ball graph is an intersection graph of a set of balls with arbitrary radii. Given a real number t > 1, we say that a subgraph G′ of a graph G is a t-spanner of G, if for eve...
We study the problem of orienting the edges of a weighted graph such that the maximum weighted outdegree of vertices is minimized. This problem, which has applications in the guar...