Rooted level-disjoint partitions of Cartesian products
Petr Gregor, Riste Ň†krekovski, Vida VukaŇ°inovińá Applied Mathematics and Computation, 2015, Vol. 266, pages: 244-258
abstract: In interconnection networks one often needs to broadcast multiple messages in parallel from a single source so that the load at each node is minimal. With this motivation we study a new concept of rooted level-disjoint partitions of graphs. In particular, we develop a general construction of level-disjoint partitions for Cartesian products of graphs that is efficient both in the number of level partitions as in the maximal height. As an example, we show that the hypercube Q‚ÄČn for every dimension n=3¬∑i^2 or n=4¬∑i^2 where i ‚Č• 0 has n level-disjoint partitions with the same root and with maximal height 3n‚ąí2. Both the number of such partitions and the maximal height are optimal. Moreover, we conjecture that this holds for any n ‚Č• 3.