We show that every triangle-free graph on the double torus is 4-colorable. This settles a problem raised by Gimbel and Thomassen [Trans. Amer. Math. Soc. 349 (1997), 4555
We study line systems in metric spaces induced by graphs. A line is a subset of vertices defined by a relation of betweeness. We show that the class of all graphs having exactly k ...
If m 2 is constant and 0 r log log n for a small positive constant , then whp a random walk with look-ahead r on a scale-free graph G = G(m, n) has cover time CG(r) (2/(mr-1(...
This work is motivated by the long-standing open problem of designing a polynomial-time algorithm that with high probability constructs an asymptotically maximum independent set in...
Mark K. Goldberg, D. Hollinger, Malik Magdon-Ismai...
The problem to determine whether a given k-colored graph is a subgraph of a properly colored interval graph has an application in DNA physical mapping. In this paper, we study the...