(3,2)-Track layout of bipartite graph subdivisions

Abstract

A (3,2)-track layout of a graph G consists of a 2-track assignment of G and an edge 3-coloring of G with no monochromatic X-crossing. This paper studies the problem of (3,2)-track layout of bipartite graph subdivisions. Recently Dujmović and Wood showed that every graph G with n vertices has a (3,2)-track subdivision of G with 4Γlog qn(G) + 3 division vertices per edge, where qn(G) is the queue number of G. This paper improves their result for the case of complete bipartite graphs, and shows that every complete bipartite graph Km,n has a (3,2)-track subdivision of Km,n with 2 Γlog qn(Km,n ) + 1 division vertices per edge, where m and n are numbers of vertices of the partite sets of K m,n with m≥n. © 2008 Springer Berlin Heidelberg.