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(d+1,2)-Track Layout of Bipartite Graph Subdivisions
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Publication Date: 2008/09/01
Online ISSN: 1745-1337
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
graph drawing, graph layout, bipartite graph, subdivision, track, track layout,
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A (k,2)-track layout of a graph G consists of a 2-track assignment of G and an edge k-coloring of G with no monochromatic X-crossing. This paper studies the problem of (k,2)-track layout of bipartite graph subdivisions. Recently V. Dujmovi and D.R. Wood showed that for every integer d ≥ 2, every graph G with n vertices has a (d+1,2)-track layout of a subdivision of G with 4 log d 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 bipartite graphs, and shows that for every integer d ≥ 2, every bipartite graph Gm,n has a (d+1,2)-track layout of a subdivision of Gm,n with 2 log d n -1 division vertices per edge, where m and n are numbers of vertices of the partite sets of Gm,n with m ≥ n.