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book thickness
Book Thickness of Subdivisions ★★
Author(s): Blankenship; Oporowski
Let be a finite undirected simple graph.
A -page book embedding of
consists of a linear order
of
and a (non-proper)
-colouring of
such that edges with the same colour do not cross with respect to
. That is, if
for some edges
, then
and
receive distinct colours.
One can think that the vertices are placed along the spine of a book, and the edges are drawn without crossings on the pages of the book.
The book thickness of , denoted by bt
is the minimum integer
for which there is a
-page book embedding of
.
Let be the graph obtained by subdividing each edge of
exactly once.
Conjecture There is a function
such that for every graph
,
![$ f $](/files/tex/43374150a8a220f67049937b9790b7d28eb17fb9.png)
![$ G $](/files/tex/b8e7ad0330f925492bf468b5c379baec88cf1b3d.png)
![$$ \text{bt}(G) \leq f( \text{bt}(G') )\enspace. $$](/files/tex/0aedb9a9a46520e4c6b7a352924b0c2e2fc329d6.png)
Keywords: book embedding; book thickness
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