论文信息 - Genus g graphs have pagenumber O( square root g)

Genus g graphs have pagenumber O( square root g)

A book embedding of a graph consists of a linear ordering of the vertices along the spine of a book and an assignment of edges to pages so that edges on the same page do not intersect. The minimum number of pages in which a graph can be embedded is its pagenumber. The following results are presented: (1) any graph of genus g has pagenumber O( square root g); and (2) most n-vertex d-regular graphs have pagenumber Omega ( square root dn/sup 1/2-1/d/).<<ETX>>

Seth M. Malitz

[1] Arnold L. Rosenberg,et al. Embedding graphs in books: a layout problem with applications to VLSI design , 1985 .

[2] Gary L. Miller,et al. The Complexity of Coloring Circular Arcs and Chords , 1980, SIAM J. Algebraic Discret. Methods.

[3] Mihalis Yannakakis,et al. Four pages are necessary and sufficient for planar graphs , 1986, Symposium on the Theory of Computing.

[4] Lenwood S. Heath. Embedding Planar Graphs in Seven Pages , 1984, FOCS.

[5] Ravi Kannan,et al. Unraveling k-page graphs , 1985, Inf. Control..

[6] Gary L. Miller,et al. On determining the genus of a graph in O(v O(g)) steps(Preliminary Report) , 1979, STOC.

[7] Paul C. Kainen,et al. The book thickness of a graph , 1979, J. Comb. Theory, Ser. B.

[8] Arnold L. Rosenberg,et al. The Diogenes Approach to Testable Fault-Tolerant Arrays of Processors , 1983, IEEE Transactions on Computers.

[9] Peter W. Shor,et al. On the pagenumber of planar graphs , 1984, STOC '84.

[10] R. P. Dilworth,et al. A DECOMPOSITION THEOREM FOR PARTIALLY ORDERED SETS , 1950 .