Given a system (G1, …, Gm) of graphs on the same vertex set V, a cooperative coloring is a choice of vertex sets I1, …, Im, such that Ij is independent in Gj and (formula presented)m j=1Ij = V . For a class G of graphs, let mG (d) be the minimal m such that every m graphs from G with maximum degree d have a cooperative coloring. We prove that Ω(log log d) ≤ mT (d) ≤ O(log d) and Ω(log d) ≤ mB(d) ≤ O(d/ log d), where T is the class of trees and B is the class of bipartite graphs.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics
- Applied Mathematics