Routing Numbers of Cycles, Complete Bipartite Graphs, and Hypercubes

The routing number rt(G) of a connected graph G is the minimum integer r so that every permutation of vertices can be routed in r steps by swapping the ends of disjoint edges. In this paper, we study the routing numbers of cycles, complete bipartite graphs, and hypercubes. We prove that rt(Cn) = n - 1 (for n 3) and for s t, rt(Ks,t) = 3s 2t + O(1). We also prove n + 1 rt(Qn) 2n - 2 for n 3. The lower bound rt(Qn) n + 1 was previously conjectured by Alon, Chung, and Graham [SIAM J. Discrete Math., 7 (1994), pp. 513

• Type: Journal
• Year: 2010
• Where: SIAMDM
• Authors: Wei-Tian Li, Linyuan Lu, Yiting Yang
• Keywords: Complete Bipartite Graphs, Fractional Routing Number, Routing Number, SIAMDM 2010